RADIOLABELED SUGARS FOR IMAGING OF FUNGAL INFECTIONS CROSS REFERENCE TO RELATED APPLICATION This application claims the benefit of the earlier filing date of U.S. provisional patent application No.62/882,023, filed August 2, 2019, which is incorporated herein by reference in its entirety. FIELD Provided herein are radiolabeled sugars, such as [ ¹⁸ F]-rhamnose and [ ¹⁸ F]-cellobiose, and methods of their use to detect and monitor a fungal infection. BACKGROUND Fungal infections remain a major health burden with very high mortality and morbidity in immunosuppressed cancer and stem cell transplant patients, in advanced HIV disease and in some congenital immunodeficiencies. A recent report estimated global mortality from fungal disease to be >1.6 million, similar to that of tuberculosis and >3-fold that of malaria (Bongomin et al., J Fungi (Basel), 3, 2017). Yet, despite the magnitude of the problem, there are currently no clinically- available fungal-specific imaging agents. FDG PET is a nonspecific technique that can be used for imaging patients with suspected active fungal infections. It cannot however, differentiate between infection and inflammation, between the various fungal pathogens or differentiate fungi from other pathogens such as bacteria. The development of fungus-specific imaging has been attempted using varying approaches including targeted antibodies (Rolle et al., Proc Natl Acad Sci U S A, 113:E1026-3, 2016), 99mTc labeled MORF oligomers targeting fungal ribosomal RNA (rRNA) (Wang et al., Nucl Med Biol, 40:89-96, 2013), and the use of radiolabeled siderophores (Haas et al., PLoS Pathog, 11: e1004568, 2015). Many of those ligands however are still in early stages of development, have been abandoned or mostly, have not been tested in humans. Thus, new fungal- specific imaging ligands are needed. SUMMARY Provided herein are new fungal-specific imaging ligands, which exploit metabolic pathways that are selectively expressed by fungi, but not by mammalian cells or bacteria. These fungal- specific imaging ligands can be used to diagnose and/or monitor a fungal infection in vivo, without the need for invasive procedures or biopsies. Disclosed herein are compounds having a formula I Formula I. With respect to Formula I, R ¹ is a radionuclide, O , , each of R ⁷ , R ⁸ , R ⁹ and R ¹⁰ independently is a radionuclide, OH, OR ⁶ , or OR ⁷ . Each of R ² , R ³ and R ⁴ independently is OH, OR ⁶ , OR ⁷ or a radionuclide. R ⁵ is H, OH, OR ⁶ , OR ⁷ or a radionuclide, with the provision that when R ¹ is X then R ⁵ is OH, OR ⁶ , OR ⁷ or a radionuclide, and when R ¹ is other than X, then R ⁵ is H, OR ⁷ , or a radionuclide. R ⁶ is acetyl, formyl, methoxyacetyl, benzoyl, haloacetyl or trialkylsilyl, and in some embodiments, R ⁶ is acetyl. And R ⁷ is triflate, mesylate or tosylate, and in some embodiments, R ⁷ is triflate. Also with respect to Formula I, one of the following conditions (a) or (b) applies: (a) if R ¹ is X then either at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is a radionuclide and the rest are OH, or at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ and the rest are OR ⁶ ; and (b) if R ¹ is other than X, then at least one of R ¹ -R ⁵ and R ⁸ -R ¹¹ is a radionuclide and the rest are OH except for R ⁵ which is either a radionuclide or H, or at least one of R ¹ -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ and the rest are OR ⁶ except for R ⁵ which is either OR ⁷ or H. In any embodiments, the radionuclide may be ¹⁸ F. In some embodiments, R ¹ is ¹⁸ F, OH, OR ⁶ , or OR ⁷ and condition (b) applies. In such embodiments, each of R ¹ , R ² , R ³ , and R ⁴ independently may be ¹⁸ F or OH; R ⁵ may be ¹⁸ F or H; and at least one of R ¹ -R ⁵ may be ¹⁸ F. And in some embodiments, R ¹ is ¹⁸ F, R ² -R ⁴ are OH, and R ⁵ is H; R ² is ¹⁸ F, R ¹ , R ³ and R ⁴ are OH, and R ⁵ is H; R ³ is ¹⁸ F, R ¹ , R ² and R ⁴ are OH, and R ⁵ is H; R ⁴ is ¹⁸ F, R ¹ , R ² and R ³ are OH, and R ⁵ is H; or R ⁵ is ¹⁸ F, and R ¹ -R ⁴ are OH. Additionally, or alternatively, the compound may have a Formula II Formula II. And with respect to Formula II, the compound may be , , , , . In other embodiments, each of R ¹ , R ² , R ³ , and R ⁴ independently is OR ⁶ or OR ⁷ ; R ⁵ is OR ⁷ or H; and at least one of R ¹ -R ⁵ is OR ⁷ . In some such embodiments, one of R ¹ -R ⁵ is OR ⁷ and the rest are OR ⁶ . And/or in some embodiments, the compound has a formula selected from . Additionally, in some embodiments, R ¹ is OR ⁷ , R ² -R ⁴ are OR ⁶ , and R ⁵ is H; R ² is OR ⁷ , R ¹ , R ³ and R ⁴ are OR ⁶ , and R ⁵ is H; R ³ is OR ⁷ , R ¹ , R ² and R ⁴ are OR ⁶ , and R ⁵ is H; R ⁴ is OR ⁷ , R ¹ , R ² and R ³ are OR ⁶ , and R ⁵ is H; or R ⁵ is OR ⁷ , and R ¹ -R ⁴ are OR ⁶ . And R ⁶ may be acetyl and R ⁷ may be triflate. In other embodiments of Formula I, the compound has a structure according to Formula IV and condition (a) applies Formula IV. In some such embodiments, each of R ² -R ⁵ and R ⁸ -R ¹¹ independently is ¹⁸ F or OH, and at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is ¹⁸ F, and in certain embodiments, one of R ² -R ⁵ and R ⁸ -R ¹¹ is ¹⁸ F and the rest of R ² -R ⁵ and R ⁸ -R ¹¹ are OH. Additionally or alternatively, the compound may have a structure according to Formula V

Formula V. With respect to Formula V, in some embodiments, R ² is ¹⁸ F and R ³ -R ⁵ and R ⁸ -R ¹¹ are OH; R ³ is ¹⁸ F and R ² , R ⁴ , R ⁵ and R ⁸ -R ¹¹ are OH; R ⁴ is ¹⁸ F and R ² , R ³ , R ⁵ and R ⁸ -R ¹¹ are OH; R ⁵ is ¹⁸ F and R ² -R ⁴ and R ⁸ -R ¹¹ are OH; R ⁸ is ¹⁸ F and R ² -R ⁵ and R ⁹ -R ¹¹ are OH; R ⁹ is ¹⁸ F and R ² -R ⁵ and R ⁸ , R ¹⁰ and R ¹¹ are OH; R ¹⁰ is ¹⁸ F and R ² -R ⁵ and R ⁸ , R ⁹ and R ¹¹ are OH; or R ¹¹ is ¹⁸ F and R ² -R ⁵ and R ⁸ -R ¹⁰ are OH. In certain embodiments, R ⁹ is ¹⁸ F and R ² -R ⁵ and R ⁸ , R ¹⁰ and R ¹¹ are OH, but in other embodiments, R ² is ¹⁸ F and R ³ -R ⁵ and R ⁸ -R ¹¹ are OH. In other embodiments of Formula IV, each of R ² -R ⁵ and R ⁸ -R ¹¹ independently is OR ⁶ or OR ⁷ , and at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ . In some embodiments, one of R ² -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ and the rest of R ² -R ⁵ and R ⁸ -R ¹¹ are OR ⁶ . And in certain embodiments, R ² is OR ⁷ and R ³ -R ⁵ and R ⁸ -R ¹¹ are OR ⁶ ; R ³ is OR ⁷ and R ² , R ⁴ , R ⁵ and R ⁸ -R ¹¹ are OR ⁶ ; R ⁴ is OR ⁷ and R ² , R ³ , R ⁵ and R ⁸ - R ¹¹ are OR ⁶ ; R ⁵ is OR ⁷ and R ² -R ⁴ and R ⁸ -R ¹¹ are OR ⁶ ; R ⁸ is OR ⁷ and R ² -R ⁵ and R ⁹ -R ¹¹ are OR ⁶ ; R ⁹ is OR ⁷ and R ² -R ⁵ and R ⁸ , R ¹⁰ and R ¹¹ are OR ⁶ ; R ¹⁰ is OR ⁷ and R ² -R ⁵ and R ⁸ , R ⁹ and R ¹¹ are OR ⁶ ; or R ¹¹ is OR ⁷ and R ² -R ⁵ and R ⁸ -R ¹⁰ are OR ⁶ . And R ⁶ may be acetyl and R ⁷ may be triflate. Also provided are compositions that include one or more radiolabeled compounds and a pharmaceutically acceptable carrier, such as water or saline. Also provided are methods of using the disclosed radiolabeled compounds to detect a fungus, in vivo to diagnose and/or monitor a fungal infection in a subject. The foregoing and other objects and features of the disclosure will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures. BRIEF DESCRIPTION OF THE DRAWINGS FIGS.1A-1F. in vitro uptake of ³ H-2-deoxygluose (2-DG) and ³ H-rhamnose in (FIG.1A) A. fumigatus (FIG.1B) E. coli (FIG.1C) S. aureus and (FIG.1D) J774 macrophages at various time-points. The net uptake of live cultures are plotted in the graphs after subtracting the background uptake by heat-killed cultures (except J774 macrophages where only uptake in live cultures was measured). (FIG.1E) In vitro uptake of ¹⁸ F-rhamnose in live and heat killed A. fumigatus and E. coli. (FIG.1F) Representative autoradiography images of in vivo uptake of ³ H-rhamnose in the lungs of healthy, poly (I:C) treated (sterile inflammation) and A. fumigatus infected mice is shown in the top panels. Bright field images of the respective lung sections are in the bottom panel. FIG.2 is a bar graph showing ³ H-L-Rhamnose results from biodistribution studies showing increased uptake in the lungs of infected compared to control mice and mice with sterile lung inflammation. FIGS.3A-3B. (FIG.3A) Representative dynamic [ ¹⁸ F]-rhamnose PET images, averaged from 520-3520 seconds post injection. Increased uptake is seen in the lungs of nasopharyngeally- infected pulmonary IA (AF NP) mice while no appreciable uptake is seen in the lungs of control or sterile lung (poly (I:C)inflammation mice. The first 520 seconds were removed from analysis to reduce potential effects of increased vascularity after injection. (FIG.3B) Time activity curve of [ ¹⁸ F]-rhamnose uptake in control, poly (I:C), and AF NP models from 0-3370 seconds post [ ¹⁸ F]-rhamnose injection. FIGS.4A-4C. In vitro uptake of ³ H-cellobiose by Aspergillus (FIG.4A) but not by macrophage (J744) cell lines (FIG.4B). (FIG.4C) Biodistribution studies show increased activity in the lungs of infected mice compared to control animals. Increased activity in the brain may reflect free labeled glucose following hydrolysis of cellobiose with secondary uptake by the brain. FIGS.5A-5B: Autoradiography and GMS staining of (FIG.5A) lung in an Aspergillus fumigatus nasopharyngeally-infected mouse and (FIG.5B) brain in an Aspergillus fumigatus IV infected mouse. GMS staining confirms the presence of fungal hyphae with corresponding 3H- Cellobiose uptake FIG.6: ¹⁸ F-deoxycellobiose with the isotope located on C2 of the first glucose molecule or ^{on the C2 of the second glucose molecule.} DETAILED DESCRIPTION I. Terms The following explanations of terms and abbreviations are provided to better describe the present disclosure and to guide those of ordinary skill in the art in the practice of the present disclosure. As used herein, “comprising” means “including” and the singular forms “a” or “an” or “the” include plural references unless the context clearly dictates otherwise. The term “or” refers to a single element of stated alternative elements or a combination of two or more elements, unless the context clearly indicates otherwise. Unless explained otherwise, all technical and scientific terms used herein have the same meaning as commonly understood to one of ordinary skill in the art to which this disclosure belongs. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure, suitable methods and materials are described below. The materials, methods, and examples are illustrative only and not intended to be limiting. Other features of the disclosure are apparent from the following detailed description and the claims. Unless otherwise indicated, all numbers expressing quantities of components, molecular weights, percentages, temperatures, times, and so forth, as used in the specification or claims are to be understood as being modified by the term “about.” Accordingly, unless otherwise indicated, implicitly or explicitly, the numerical parameters set forth are approximations that may depend on the desired properties sought and/or limits of detection under standard test conditions/methods. When directly and explicitly distinguishing embodiments from discussed prior art, the embodiment numbers are not approximates unless the word “about” is recited. Unless explained otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure, suitable methods and materials are described below. The materials, methods, and examples are illustrative only and not intended to be limiting. When chemical structures are depicted or described, unless explicitly stated otherwise, all carbons are assumed to include implicit hydrogens such that each carbon conforms to a valence of four. For example, in the structure on the left-hand side of the schematic below there are nine hydrogen atoms implied. The nine hydrogen atoms are depicted in the right-hand structure. Sometimes a particular atom in a structure is described in textual formula as having a hydrogen or hydrogen atoms, for example -CH ₂ CH ₂ -. It will be understood by a person of ordinary skill in the art that the aforementioned descriptive techniques are common in the chemical arts to provide brevity and simplicity to description of organic structures. Administration: To provide or give a subject an agent, such as a radiolabeled sugar provided herein and/or an anti-fungal agent, by any effective route. Exemplary routes of administration include, but are not limited to, topical, injection (such as subcutaneous, intramuscular, intradermal, intraperitoneal, intraosseous, intra-arterial, and intravenous), oral, ocular, sublingual, rectal, transdermal, intranasal, vaginal and inhalation routes. Alkyl: A saturated aliphatic hydrocarbyl group having from 1 to 25 (C _1-25 ) or more carbon atoms, more typically 1 to 10 (C1-10) carbon atoms such as 1 to 6 (C _1-6 ) carbon atoms or 1 to 4 (C _1-4 ) carbon atoms. This term includes, by way of example, linear and branched hydrocarbyl groups such as methyl (CH ₃ ), ethyl (-CH ₂ CH ₃ ), n-propyl (-CH ₂ CH ₂ CH ₃ ), isopropyl (-CH(CH ₃ ) ₂ ), n-butyl (-CH ₂ CH ₂ CH ₂ CH ₃ ), isobutyl (-CH ₂ CH ₂ (CH ₃ ) ₂ ), sec-butyl (-CH(CH ₃ )(CH ₂ CH ₃ ), or t-butyl (- C(CH ₃ )3). Contact: Placement in direct physical association, including a solid or a liquid form. Contacting can occur in vitro or ex vivo, for example, by adding a reagent to a sample, or in vivo by administering to a subject. Detect or measure: To determine if a particular agent (e.g., fungal infection, radiolabeled sugar provided herein) is present or absent, and in some examples further includes semi- quantification or quantification of the agent if detected. Effective amount: An amount of a composition that alone, or together with an additional therapeutic agent(s) sufficient to achieve a desired effect, for example in vivo The effective amount of the agent (such as an anti-fungal agent) can be dependent on several factors, including, but not limited to the subject being treated (e.g., whether the subject is immune compromised), the severity, stage, and type of fungal infection being treated, the particular therapeutic agent, and the manner of administration. Effective amounts also can be determined through various in vitro, in vivo or in situ immunoassays. One or more anti-fungal agents can be administered in a single dose, or in several doses, as needed to obtain the desired response. In one example, an effective amount or concentration is one that is sufficient to treat a fungal infection in a subject, for example by reducing or inhibiting one or more symptoms associated with the infection. The infection and symptoms need not be completely eliminated for the method to be effective. For example, administering one or more anti-fungal agents to a subject can substantially decrease the fungal infection (or one or more signs or symptoms of the infection) in the subject, such as a decrease of at least 20%, at least 50%, at least 80%, at least 90%, at least 95%, at least 98%, or even at least 100%, as compared to the amount present prior to administration of the ng one or more anti-fungal agents. Fungus: A member of the group of eukaryotic organisms that includes chitin in their cell walls. Includes fungal organisms that can infect a subject, such as mammals and birds. Fungal infections invade one or more tissues causing infection, for example in the skin or internal organs such as the blood, kidney, heart, esophagus, lungs, sinuses, gastrointestinal tract, and central nervous system (e.g., brain, spinal cord). Exemplary fungi that can be diagnosed or treated using the methods provided herein include, but are not limited to, Aspergillus (which can cause Aspergillosis), such as A. fumigatus, A. flavus, A. terreus, and A. niger; Candida (which can cause candidiasis), such as C. albicans; Cryptococcus (which can cause Cryptococcosis), such as C. neoformans and C. gattii; and Mucormycetes (which can cause mucormycosis, sometimes called zygomycosis), such as Rhizopus species, Mucor species, Rhizomucor species, Syncephalastrum species, Cunninghamella bertholletiae, Apophysomyces species, and Lichtheimia (formerly Absidia). Halo: Fluoro, chloro, bromo or iodo. Pharmaceutically acceptable carrier: The pharmaceutically acceptable carriers (vehicles) useful in this disclosure are conventional. Remington’s Pharmaceutical Sciences, by E. W. Martin, Mack Publishing Co., Easton, PA, 19th Edition (1995), describes compositions and formulations suitable for pharmaceutical delivery of one or more therapeutic compounds, such as one or more radiolabeled compounds provided herein. In general, the nature of the carrier will depend on the particular mode of administration being employed. For instance, parenteral formulations usually comprise injectable fluids that include pharmaceutically and physiologically acceptable fluids such as water, physiological saline, balanced salt solutions, aqueous dextrose, glycerol or the like as a vehicle. For solid compositions (for example, powder, pill, tablet, or capsule forms), conventional non-toxic solid carriers can include, for example, pharmaceutical grades of mannitol, lactose, starch, or magnesium stearate. In addition to biologically-neutral carriers, pharmaceutical compositions to be administered can contain minor amounts of non-toxic auxiliary substances, such as wetting or emulsifying agents, preservatives, and pH buffering agents and the like, for example sodium acetate or sorbitan monolaurate. Precursor and precursor compound: Compounds that are used to make a radiolabeled compound, but typically do not comprise a radionuclide themselves. A person of ordinary skill in the art understands that because transport of radioactive compounds may be problematic, due to transport restrictions and that fact that the radioactive isotope decays over time, the precursor compound may be prepared, stored and/or transported, and the radionuclide is added prior to use, such as by an end user. Typically, a precursor compound comprises a leaving group that can exchanged or displaced when the radionuclide is introduced. The precursor compound also may comprise one or more protecting groups that protect other functional groups when the radionuclide is introduced, and can be removed prior to use. Radiolabeled: A compound that comprises a radionuclide. Radionuclide: A radioactive isotope. For example, ¹⁸ F is a radionuclide of fluorine. Sample: A sample of biological material obtained from a subject, which can include cells (such as fungal cells), proteins, nucleic acid molecules (such as DNA and/or RNA). Biological samples include all clinical samples useful for detection of disease, such as a fungal infection, in subjects. Appropriate samples include any conventional biological samples, including clinical samples obtained from a human or veterinary subject. Exemplary samples include, without limitation, cells, cell lysates, blood smears, cytocentrifuge preparations, cytology smears, bodily fluids (e.g., blood, plasma, serum, stool/feces, saliva, sputum, urine, bronchoalveolar lavage, cerebrospinal fluid (CSF), nasal swabs, etc.), or fine-needle aspirates. Samples may be used directly from a subject, or may be processed before analysis (such as concentrated, diluted, purified). In a particular example, a sample or biological sample is obtained from a subject having, suspected of having, or at risk of having a fungal infection. Subject or patient: A term that includes human and non-human mammals. In one example, the subject is a human or veterinary subject, such as a mouse, non-human primate, cow, pig, rabbit, rat, horse, cat, dog, and the like. In some examples, the subject is a mammal (such as a human) who has a fungal infection, or is being treated for a fungal infection. In some examples, the subject is immune compromised. In some examples, the subject is immune compromised and has a fungal infection, such as invasive aspergillosis. In some examples, a subject analyzed with the disclosed methods is one who has received a transplant (e.g., transplant of at least one of a stem cell or solid organ, such as lung, heart, liver, kidney, pancreas, or intestine). In some examples, a subject analyzed with the disclosed methods is one who has a primary immunodeficiency (examples of primary immunodeficiency diseases include those listed in Al-Herz et al. (Frontiers in Immunology, volume 5, article 162, April 22, 2014, herein incorporated by reference in its entirety), e.g., T-B+ SCID, T-B- SCID, WHIM syndrome, IL-7 receptor severe combined immune deficiency (SCID), Adenosine deaminase deficiency (ADA) SCID, Purine nucleoside phosphorylase (PNP) deficiency, Wiskott-Aldrich syndrome (WAS), Chronic granulomatous disease (CGD), Leukocyte adhesion deficiency (LAD), Duchenne muscular dystrophy, Glycogen storage disease type IA, Retinal Dystrophy, and X-linked immunodeficiency with magnesium defect, Epstein-Barr virus infection, and neoplasia (XMEN)). In some examples, a subject analyzed with the disclosed methods is one who has HIV or AIDS. In some examples, a subject analyzed with the disclosed methods is one who has cancer, such as a cancer of the lung, liver, pancreas, breast, prostate, ovary, colon, rectum, head and neck, brain, bone, or blood. The terms “ ¹⁸ F-rhamnose” and “[ ¹⁸ F]-rhamnose” include ¹⁸ F-labeled rhamnose and deoxyrhamnose analogs, such as, but not limited to, 6- ¹⁸ F-rhamnose and ¹⁸ F-deoxyrhamnose analogs where the ¹⁸ F is at the 1, 2, 3, 4, or 5 position. The term “ ¹⁸ F-cellobiose” and “[ ¹⁸ F]-cellobiose” include ¹⁸ F-labeled cellobiose and deoxycellobiose analogs, such as, but not limited to, 6- ¹⁸ F-cellobiose, 12- ¹⁸ F-cellobiose, and ¹⁸ F- deoxycellobiose analogs where the ¹⁸ F is at the 1, 2, 3, 8, 9, or 10 positions. II. Overview The inventors identified sugars and other molecules involved in the metabolic pathways of clinically-relevant fungal infections, and generated radiolabeled versions (3H or 14C) that were tested for in vitro uptake in bacteria (gram-negative, gram-positive, Pseudomonas aeruginosa), macrophages (J774 cell line) and m clinically-relevant fungal strains including Aspergillus, Rhizomucor, Cryptococcus and Candida albicans. Organisms and cells were exposed to the radiolabeled compounds and the in vitro uptake was measured (retained radioactivity after incubation and washing of the cultures measured using a beta counter). If positive uptake in the fungi was observed with no or only low uptake in bacteria and mammalian cells, organ biodistribution studies and autoradiography were used to determine specific uptake in different animal models of fungal infection. For the biodistribution and autoradiography studies showing specific uptake of the radioactive molecules by fungal-infected animals (i.e., retained radioactivity in the lungs in the infected animals but not in the control animals), the ligand(s) specific for each type of fungi was radiolabeled with 18F or other PET isotopes. Using the radiolabeled ligand(s), live PET imaging is performed on infected mice using a microPET/CT scanner. This is done by injecting the radioactive ligand intravenously through the tail vein and then positioning the animals inside the microPET/CT gantry and obtaining CT scan images as well as PET emission data. The images are reconstructed and analyzed using special software. To confirm specificity for fungal infection, in vivo uptake of the ligand(s) in animal models of sterile inflammation, as well as models of bacterial infection (gram positive and gram negative bacteria) are performed. Three main mouse models were developed: (1) Aspergillus lung infection (nasopharyngeal administration of 30µl suspension of Aspergillus conidia), (2) Aspergillus hematogenous spread (intravenous administration of 100µl of fungal suspension via the tail vein) and (3) sterile lung inflammation model (induced by nasopharyngeal administration of 50-100µg of poly (I:C) suspension in 30µl of sterile PBS; poly(I:C) is a synthetic double stranded RNA which activates Toll-like receptors-3 (TLR3), thereby inducing signaling via multiple inflammatory pathways). Additional mouse models included Gram negative (E. coli) and gram positive (S. aureus) bacterial infection models (myositis induced by injection of 107-109 CFU of E. coli or Staphylococcus aureus intramuscularly into the caudal thigh region (hind limb)), a model of subcutaneous Aspergillus infection (200µl suspension containing 5x 105 to 5x 107 conidia injected subcutaneously, in the right dorsum) and a model of contralateral sterile inflammation (heat killed conidia + complete Freund’s adjuvant (CFA)). Other fungal mouse models besides Aspergillus include Candida albicans (intravenous injection of 100-150µl of Candida culture containing a CFU of 103-109) and Cryptococcus neoformans (30µl suspension of fungal cells administered through the posterior pharyngeal method) infected models. Two sugars, L-rhamnose and cellobiose were radiolabeled and can be used as PET ligands. III. Compounds Disclosed herein are radiolabeled compounds and precursors thereof. Radiolabeled compounds comprise a radionuclide, for example ¹⁸ F. The radiolabeled compounds are useful as for diagnosing certain infections, such as fungal infections, in a patient. In some embodiments, the compounds are analogs and/or derivatives of sugars that are metabolized by fungi, and may be selectively metabolized by the fungi, such that the patient does not substantially metabolize the sugar. This results in the radiolabeled metabolites selectively accumulating in the fungi, thereby identifying the fungal infection. In some embodiments, the compound has a formula I Formula I. With respect to Formula I: R ¹ is a radionuclide, OH, OR ⁶ , OR ⁷ or X; X is where each of R ⁷ , R ⁸ , R ⁹ and R ¹⁰ independently is a radionuclide, OH, OR ⁶ , or OR ⁷ ; each of R ² , R ³ and R ⁴ independently is OH, OR ⁶ , OR ⁷ or a radionuclide; R ⁵ is H, OH, OR ⁶ , OR ⁷ or a radionuclide, with the proviso that when R ¹ is X then R ⁵ is OH, OR ⁶ , OR ⁷ or a radionuclide, and when R ¹ is other than X, (i.e., R ¹ is a radionuclide, OH, OR ⁶ , OR ⁷ ) then R ⁵ is H, OR ⁷ , or a radionuclide; R ⁶ is a suitable protecting group, and may be an ester or silyl protecting group, such as acetyl (CH ₃ C(=O)-; Ac), formyl, methoxyacetyl, benzoyl, haloacetyl (such as trifluoroacetyl, chloroacetyl, dichloroacetyl, or trichloroacetyl) or trialkylsilyl (such as trimethyl silyl or triethyl silyl), and in certain embodiments, R ⁶ is acetyl; R ⁷ is a suitable leaving group, such as triflate (CF3SO2; Tr), mesylate (CH ₃ SO2) or tosylate (CH ₃ PHSO ₂ ), and in certain embodiments, R ⁷ is triflate; Also, with respect to Formula I the following conditions apply: (a) if R ¹ is X then either at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is a radionuclide and the rest are OH, or at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ and the rest are OR ⁶ ; and (b) if R ¹ is other than X, then at least one of R ¹ -R ⁵ and R ⁸ -R ¹¹ is a radionuclide and the rest are OH except for R ⁵ which is either a radionuclide or H; or at least one of R ¹ -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ and the rest are OR ⁶ except for R ⁵ which is either OR ⁷ or H. In some embodiments, R ¹ is OR ⁶ , OR ⁷ , X; each R ² -R ⁴ independently is OR ⁶ or OR ⁷ ; R ⁵ is H, OR ⁶ or OR ⁷ ; and, if present, each of R ⁷ , R ⁸ , R ⁹ and R ¹⁰ independently is OR ⁶ or OR ⁷ . In other embodiments, R ¹ is OH, a radionuclide, or X; each R ² -R ⁴ independently is OH or a radionuclide; R ⁵ is H, OH or a radionuclide; and, if present, each of R ⁷ , R ⁸ , R ⁹ and R ¹⁰ independently is OH or a radionuclide. In any embodiments, the radionuclide may be ¹⁸ F. I. Rhamnose analogs In some embodiments of Formula I, the compound is a rhamnose analog. In such embodiments, R ¹ is other than X, i.e., R ¹ is a radionuclide, OH, OR ⁶ , or OR ⁷ and condition (b) applies. In any embodiments, the rhamnose analog may be an L-Rhamnose analog. i) radiolabeled rhamnose In some embodiments, the rhamnose analog is a radiolabeled analog, such as an ¹⁸ F radiolabeled rhamnose or deoxyrhamnose analog. In such embodiments, each of R ¹ , R ² , R ³ , and R ⁴ independently is ¹⁸ F or OH, and R ⁵ is ¹⁸ F or H, where at least one of R ¹ -R ⁵ is ¹⁸ F. In some embodiments, one of R ¹ -R ⁵ is ¹⁸ F. In some embodiments, the compound is ¹⁸ F radiolabeled L-Rhamnose analog and has a structure according to Formula II: Formula II. With respect to Formula II, R ¹ -R ⁴ are ¹⁸ F or OH and R ⁵ is ¹⁸ F or H, where at least one, and optionally exactly one of R ¹ -R ⁵ is ¹⁸ F. In an embodiment of Formulas I or II, R ¹ is ¹⁸ F, R ² -R ⁴ are OH, and R ⁵ is H. In an embodiment of Formulas I or II, R ² is ¹⁸ F, R ¹ , R ³ and R ⁴ are OH, and R ⁵ is H. In an embodiment of Formulas I or II, R ³ is ¹⁸ F, R ¹ , R ² and R ⁴ are OH, and R ⁵ is H. In an embodiment of Formulas I or II, R ⁴ is ¹⁸ F, R ¹ , R ² and R ³ are OH, and R ⁵ is H. In an embodiment of Formulas I or II, R ⁵ is ¹⁸ F, and R ¹ -R ⁴ are OH. In a particular embodiment of Formula II, R ² is ¹⁸ F, R ¹ , R ³ and R ⁴ are OH, and R ⁵ is H; or R ³ is ¹⁸ F, R ¹ , R ² and R ⁴ are OH, and R ⁵ is H; or R ⁵ is ¹⁸ F, and R ¹ -R ⁴ are OH. Exemplary Rhamnose analogs according to Formula II: ii) Radiolabeled rhamnose precursor In other embodiments of Formula I, the compound is a precursor compound to a radiolabeled rhamnose analog. In such embodiments, each of R ¹ , R ² , R ³ , and R ⁴ independently is OR ⁶ or OR ⁷ , and R ⁵ is OR ⁷ or H, where at least one of R ¹ -R ⁵ is OR ⁷ , and R ⁶ and R ⁷ are as previously defined. In some embodiments, exactly one of R ¹ -R ⁵ is OR ⁷ , and the rest are OR ⁶ . The Rhamnose precursor compound may have a structure according to any one of Formulas III-a to III-e: . In an embodiment of Formulas I or III-a to III-e, R ¹ is OR ⁷ , R ² -R ⁴ are OR ⁶ , and R ⁵ is H. In an embodiment of Formulas I or III-a to III-e, R ² is OR ⁷ , R ¹ , R ³ and R ⁴ are OR ⁶ , and R ⁵ is H. In an embodiment of Formulas I or III-a to III-e, R ³ is OR ⁷ , R ¹ , R ² and R ⁴ are OR ⁶ , and R ⁵ is H. In an embodiment of Formulas I or III-a to III-e, R ⁴ is OR ⁷ , R ¹ , R ² and R ³ are OR ⁶ , and R ⁵ is H. In an embodiment of Formulas I or III-a to III-e, R ⁵ is OR ⁷ , and R ¹ -R ⁴ are OR ⁶ . In some embodiments of Formulas I or III-a to III-e, R ⁶ is acetyl. In some embodiments, R ⁷ is triflate. And in certain embodiments, R ⁶ is acetyl and R ⁷ is triflate. Exemplary Rhamnose analogs according to Formulas III-a to III-e include: , , , , II. Cellobiose analogs In some embodiments of Formula I, the compound is a cellobiose analog. In such embodiments, R ¹ is X, leading to compounds according to Formula IV: Formula IV. With respect to Formula IV, R ² -R ¹¹ are as previously defined for Formula I, and condition (a) applies. In some embodiments, the cellobiose analog is a D-cellobiose analog. i) Radiolabeled Cellobiose In some embodiments of Formula IV, the cellobiose analog is a radiolabeled cellobiose analog, such as an ¹⁸ F radiolabeled cellobiose or deoxycellobiose analog. In some embodiments, each of R ² -R ⁵ and R ⁸ -R ¹¹ independently is ¹⁸ F or OH, where at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is ¹⁸ F. In some embodiments, one of R ² -R ⁵ and R ⁸ -R ¹¹ is ¹⁸ F and the rest of R ² -R ⁵ and R ⁸ -R ¹¹ are OH. In some embodiments, the ¹⁸ F radiolabeled cellobiose or deoxycellobiose analog may have a Formula V

. With respect to Formula IV, R ² -R ⁵ and R ⁸ -R ¹¹ are ¹⁸ F or OH, where at least one, and optionally exactly one of R ² -R ⁵ and R ⁸ -R ¹¹ is ¹⁸ F. In an embodiment of Formulas IV and V, R ² is ¹⁸ F and R ³ -R ⁵ and R ⁸ -R ¹¹ are OH. In an embodiment of Formulas IV and V, R ³ is ¹⁸ F and R ² , R ⁴ , R ⁵ and R ⁸ -R ¹¹ are OH. In an embodiment of Formulas IV and V, R ⁴ is ¹⁸ F and R ² , R ³ , R ⁵ and R ⁸ -R ¹¹ are OH. In an embodiment of Formulas IV and V, R ⁵ is ¹⁸ F and R ² -R ⁴ and R ⁸ -R ¹¹ are OH. In an embodiment of Formulas IV and V, R ⁸ is ¹⁸ F and R ² -R ⁵ and R ⁹ -R ¹¹ are OH. In an embodiment of Formulas IV and V, R ⁹ is ¹⁸ F and R ² -R ⁵ and R ⁸ , R ¹⁰ and R ¹¹ are OH. In an embodiment of Formulas IV and V, R ¹⁰ is ¹⁸ F and R ² -R ⁵ and R ⁸ , R ⁹ and R ¹¹ are OH. In an embodiment of Formulas IV and V, R ¹¹ is ¹⁸ F and R ² -R ⁵ and R ⁸ -R ¹⁰ are OH. In particular embodiments of Formulas IV and V, R ⁹ is ¹⁸ F and R ² -R ⁵ and R ⁸ , R ¹⁰ and R ¹¹ are OH, and in another particular embodiment of Formulas IV and V, R ² is ¹⁸ F and R ³ -R ⁵ and R ⁸ - R ¹¹ are OH. Exemplary compounds according to Formulas IV and V include:

ii. Radiolabeled cellobiose precursor In other embodiments of Formula IV, the compound is a precursor compound to a radiolabeled cellobiose analog. In such embodiments, each of R ² -R ⁵ and R ⁸ -R ¹¹ independently is OR ⁶ or OR ⁷ , where at least one of R ² -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ . In some embodiments, one of R ² -R ⁵ and R ⁸ -R ¹¹ is OR ⁷ and the rest of R ² -R ⁵ and R ⁸ -R ¹¹ are OR ⁶ . The cellobiose precursor analog may have a structure according to any one of Formulas VI- a to VI-h:

, In an embodiment of Formulas IV and VI-a to VI-h, R ² is OR ⁷ and R ³ -R ⁵ and R ⁸ -R ¹¹ are OR ⁶ . In an embodiment of Formulas IV and VI-a to VI-h, R ³ is OR ⁷ and R ² , R ⁴ , R ⁵ and R ⁸ -R ¹¹ are OR ⁶ . In an embodiment of Formulas IV and VI-a to VI-h, R ⁴ is OR ⁷ and R ² , R ³ , R ⁵ and R ⁸ -R ¹¹ are OR ⁶ . In an embodiment, of Formulas IV and VI-a to VI-h R ⁵ is OR ⁷ and R ² -R ⁴ and R ⁸ -R ¹¹ are OR ⁶ . In an embodiment of Formulas IV and VI-a to VI-h, R ⁸ is OR ⁷ and R ² -R ⁵ and R ⁹ -R ¹¹ are OR ⁶ . In an embodiment of Formulas IV and VI-a to VI-h, R ⁹ is OR ⁷ and R ² -R ⁵ and R ⁸ , R ¹⁰ and R ¹¹ are OR ⁶ . In an embodiment, of Formulas IV and VI-a to VI-h R ¹⁰ is OR ⁷ and R ² -R ⁵ and R ⁸ , R ⁹ and R ¹¹ are OR ⁶ . In an embodiment of Formulas IV and VI-a to VI-h, R ¹¹ is OR ⁷ and R ² -R ⁵ and R ⁸ -R ¹⁰ are OR ⁶ . In particular embodiments of Formulas IV and VI-a to VI-h, R ⁹ is OR ⁷ and R ² -R ⁵ and R ⁸ , R ¹⁰ and R ¹¹ are OR ⁶ , and in another particular embodiment, R ² is OR ⁷ and R ³ -R ⁵ and R ⁸ -R ¹¹ are OR ⁶ . In some embodiments of Formulas IV and VI-a to VI-h, R ⁶ is acetyl. In some embodiments, R ⁷ is triflate. And in certain embodiments, R ⁶ is acetyl and R ⁷ is triflate. Exemplary compounds according to Formulas IV and VI-a to VI-h include: IV. Compositions Also provided are compositions that include one or more of the radiolabeled compounds herein, such as an [ ¹⁸ F]-cellobiose or [ ¹⁸ F]-rhamnose compound. In some examples such a composition includes a pharmaceutically acceptable carrier, such as water or saline. Thus, in some examples the composition is a liquid composition, for example suitable for injection into a subject. In some examples the composition is frozen or freeze-dried. In some examples, the composition is present in a container, such as a glass or plastic vial. V. Methods of Detecting Fungi Provided here are in vivo and ex vivo/in vitro methods of using one or more of the radiolabeled compounds provided herein, such as [ ¹⁸ F]-cellobiose or [ ¹⁸ F]-rhamnose, to detect a fungus. The methods can detect any fungus of interest, such as an Aspergillus, Candida, Cryptococcus, or Mucormycetes. In some examples, the method detects Aspergillus, such as A. fumigatus, A. flavus, A. terreus, or A. niger. In some examples, the method detects Candida, such as C. albicans. In some examples, the method detects Cryptococcus, such as C. neoformans or C. gattii. In some examples, the method detects Mucormycetes, such as a Rhizopus, Mucor, Rhizomucor, Syncephalastrum, Cunninghamella bertholletiae, Apophysomyces, or Lichtheimia. The method can include contacting the fungus in vivo with one or more compounds or compositions provided herein, thereby detecting the fungus. In some examples, the method is an in vivo method of detecting a fungal infection in a subject (such as any fungus provided above, or listed in Table 1 below; thus in some examples, the subject is one having a disease listed in Table 1). In some examples the subject is a mammal or bird or fish, such a human or veterinary subject. In some examples, the subject is immunocompromised, such as a cancer patient (e.g., one undergoing chemo and/or radiation therapy), a subject who has received a transplant (e.g., transplant of at least one of a stem cell or solid organ such as a lung, heart, liver, kidney, pancreas, or intestine), a subject having a primary immunodeficiency (examples of primary immunodeficiency diseases include those listed in Al- Herz et al. (Frontiers in Immunology, volume 5, article 162, April 22, 2014, herein incorporated by reference in its entirety), e.g., T-B+ SCID, T-B- SCID, WHIM syndrome, IL-7 receptor severe combined immune deficiency (SCID), Adenosine deaminase deficiency (ADA) SCID, Purine nucleoside phosphorylase (PNP) deficiency, Wiskott-Aldrich syndrome (WAS), Chronic granulomatous disease (CGD) , Leukocyte adhesion deficiency (LAD), Duchenne muscular dystrophy, Glycogen storage disease type IA, Retinal Dystrophy, and X-linked immunodeficiency with magnesium defect, Epstein-Barr virus infection, and neoplasia (XMEN)) or a subject with HIV. In such examples, the contacting includes administering one or more compounds or compositions provided herein (such as 1, 2, 3, 4 or 5 compositions) to a subject, and the method further includes subsequently performing diagnostic imaging (such as nuclear imaging) of the subject, thereby detecting the fungal infection in the subject. For example, the diagnostic imaging can be performed at least 15 minutes, at least 20 minutes, at least 30 minutes, at least 45 minutes, at least 60 minutes, or at least 120 minutes, such as 15 to 30, 15 to 60, 30 to 60, 30 to 120, or 60 to 120 minutes after administering the one or more compounds to the subject. In some examples, administering includes injection into the subject, such as IV administration. In some examples, depending on the size and weight of the subject, a least 1 millicurie, at least 2 millicuries, at least 3 millicuries, at least 4 millicuries, at least 5 millicuries, at least 10 millicuries, such as1-3, 1-5, 1-10, 1-20, 5-20 or 5-10 millicuries of the one or more compounds is administered to the subject. In some examples, diagnostic imaging of the subject includes nuclear imaging of the brain, lungs, heart, sinuses, and/or abdomen of the subject. In some examples, positron emission tomography (PET) nuclear imaging technology is used. PET enables visualization of metabolic processes in vivo. PET imaging detects pairs of gamma rays emitted indirectly by a positron- emitting radionuclide (such as ¹⁸ F in [ ¹⁸ F]-cellobiose or [ ¹⁸ F]-rhamnose). PET systems have sensitive detector panels to capture gamma ray emissions from inside the body and use software to plot and triangulate the source of the emissions, creating 3-D computed tomography images of the tracer concentrations within the body. The in vivo methods can be used to detect a fungal infection in a subject, such as in the blood, kidney, heart, esophagus, lungs, sinuses, gastrointestinal tract, and/or central nervous system (e.g., brain, spinal cord). Detection of the administered radiolabeled compound(s) provided herein, such as [ ¹⁸ F]-cellobiose or [ ¹⁸ F]-rhamnose, indicates the presence (and location) of a fungal infection. In some examples, such methods are used to monitor treatment of a fungal infection. Thus, in some examples, the subject is one who has previously been treated with one or more anti- fungal compositions. Also provided are ex vivo or in vitro methods of detecting a fungus, for example by incubating or contacting the one or more radiolabeled compounds with a sample containing the fungus, for example a biological sample obtained from a subject, thereby detecting the fungal infection. The method can further include detecting the uptake of the radiolabeled compound(s) provided herein, such as [ ¹⁸ F]-cellobiose or [ ¹⁸ F]-rhamnose, in the sample, for example by using a beta counter, radioTLC or autoradiography. VI. Methods of Treatment Also provided are methods of treating a subject diagnosed with fungal infection using the methods provided herein. In some examples, treatment includes administering to the subject a therapeutically effective amount of one or more anti-fungal compounds. Any conventional methods of administration can be used, such as injection, inhalation, and oral administration. Exemplary anti-fungal compounds that can be administered include therapeutically effective amounts of one or more of itraconazole, a corticosteroid, voriconazole, amphotericin B, posaconazole, isavuconazole, caspofungin, micafungin, clotrimazole, miconazole, nystatin, fluconazole, anidulafungin and flucytosine. Exemplary diseases and treatments are provided in Table 1. Table 1: Fungal diseases affecting patients with weakened immune system

VII. Examples Example 1 Synthesis of 2-deoxy-2-fluororhamnose (3R,4R,5S,6S)-6-methyltetrahydro-2H-pyran-2,3,4,5-tetrayl tetraacetate Compound 2 was prepared according to the method described by Toyokuni et al., Mol Imaging Biol.2004, 6(5):324-330. Briefly, L-Rhamnose (10 g, 54.9 mmol) was carefully added in portions (3 portions in 15 minutes) to a stirring solution of iodine (0.125 g, 0.49 mmol) in acetic anhydride (60 mL) under a cool water bath (10-15 °C). The resulting mixture was allowed to warm up to room temperature and stirred for 2 hours. The mixture was then poured on a mixture of crushed ice and saturated aqueous Na ₂ S ₂ O ₃ (250 mL, 1:1 mixture) with vigorous stirring. To the resulting light yellow mixture under ice-water bath, NaHCO3 was added portion wise until no more CO ₂ was released. The crude product was extracted with CH ₂ Cl ₂ (150 mL × 3). The organic layer was combined, washed with saturated NaHCO3 solution and water (400 mL each), and dried over anhydrous Na2SO4. Crude product 2 was obtained by removing the volatiles under reduced pressure (19.33 g, 95.4% yield, a : b anomer ratio = 3 : 1). 1H NMR (400 MHz, Chloroform-d) d 6.02 (d, J = 1.9 Hz, 1H), 5.83 (s, 0.34H), 5.48 (s, 0.34H), 5.36 – 5.28 (m, 1H), 5.26 (dd, J = 3.5, 2.0 Hz, 1H), 5.18 – 5.05 (m, 1.7H), 4.00-3.90 (m, 1H), 3.72-3.62 (m, 0.36H), 2.23 (s, 4H), 2.22, (s, 1H), 2.20 (s, 3H), 2.15 (s, 3H), 2.11 (s, 1H), 2.07 (s, 4H), 2.01 (s, 4H), 1.30 (d, J = 6.2 Hz, 1H), 1.25 (d, J = 6.2 Hz, 3H). MS (ESI) calculated mass for the parent C14H20O9332.11 [M], found 355.00 [M+Na]. (5S,6S,7R,7aR)-2-ethoxy-2,5-dimethyltetrahydro-5H-[1,3]dioxo lo[4,5-b]pyran-6,7-diyl diacetate To a solution of Compound 2 (19.33 g, 58.2 mmol) in glacial acetic acid (20 mL) and acetic anhydride (1.6 mL) was added HBr in acetic acid (30%, 20 mL) dropwise under ice water bath and vigorous stirring. The resulting mixture was stirred under room temperature overnight and slowly quenched with pre-cooled saturated NaHCO ₃ solution (500 mL). The brominated intermediate was extracted with CHCl3 (200 mL ×2). The organic layer was combined, dried over anhydrous Na ₂ SO ₄ . The bromide intermediate was obtained by removing the volatiles under reduced pressure as a yellow oil (17.8 g). The oily bromide intermediate was dissolved in a mixture of anhydrous acetonitrile (8 mL), and 2,4,6-collidine (11 mL), ethanol (200 proof, 13 mL) was added. The resulting mixture was stirred under room temperature overnight, diluted with CH ₂ Cl ₂ (300 mL) and washed water (300 mL × 2) and brine (200 mL). The organic layer was dried over anhydrous Na2SO4. Crude product was obtained by removing the volatiles under reduced pressure. Product 3 was purified by flash column chromatography with hexane / ethyl acetate 4/1 to 2/1 gradient (7.8 g, 42.2% yield for 2 steps). 1H NMR (400 MHz, Chloroform-d) d 5.41 (d, J = 2.4 Hz, 1H), 5.16 – 5.02 (m, 2H), 4.59 (dd, J = 3.8, 2.4 Hz, 1H), 3.65 – 3.47 (m, 3H), 2.12 (s, 3H), 2.07 (s, 3H), 1.75 (s, 3H), 1.30 – 1.14 (m, 6H). MS (ESI) calculated mass for the parent C14H22O8318.13 [M], found 341.00 [M+Na]. (3R,4S,5S,6S)-3-hydroxy-6-methyltetrahydro-2H-pyran-2,4,5-tr iyl triacetate Hydrochloric acid (1N, 10 mL) was added to a solution of the orthoester 3 (7 g, 22.0 mmol) and acetone (15 mL). The mixture was stirred under room tempertaure for 10 minutes and volatiles were removed under reduced pressure. The resulting crude product was dissolved in CH ₂ Cl ₂ (150 mL) and washed with water (150 mL × 2). The organic layer was dried over anhydrous Na2SO4. Crude product was obtained by removing the volatiles under reduced pressure. Product 4 was purified by flash column chromatography with hexane / ethyl acetate 4/1 to 1/1 gradient (3.15 g, 49.3% yield). 1H NMR (400 MHz, Chloroform-d) d 5.76 (s, 1H), 5.15 (t, J = 9.8 Hz, 1H), 4.99 (dd, J = 9.9, 3.0 Hz, 1H), 4.22 – 4.15 (m, 1H), 3.65 (dq, J = 9.3, 6.2 Hz, 1H), 2.5-2.25 (br s, 1 H), 2.17 (s, 3H), 2.11 (s, 3H), 2.06 (s, 3H), 1.27 (d, J = 6.2 Hz, 3H). MS (ESI) calculated mass for the parent C12H18O8290.10 [M], found 313.00 [M+Na]. (3S,4S,5S,6S)-3-hydroxy-6-methyltetrahydro-2H-pyran-2,4,5-tr iyl triacetate The triacetate 4 (1.0 g, 3.19 mmol) was dissolved in anhydrous CH ₂ Cl2 (20 mL) and anhydrous pyridine (3.5 mL) and cooled with ice-salt bath. Trifluoromethanesulfonic anhydride (4.5 g, 15.97 mmol) in CH ₂ Cl2 (10 mL) was added dropwise. The mixture was stirred under room temperature for 20 minutes, sequentially washed with HCl (0.3 M, 30 mL), saturated NaHCO3 (30 mL) and brine (30 mL). The organic layer was dried over anhydrous Na2SO4. The crude triflate was obtained by removing the volatiles under reduced pressure. The crude triflate (1.35 g) was stirred with acetonitrile (30 mL) and tetrabutylammonium nitrate (4.59 g, 16.0 mmol) under room temperature for 1 hour. Crude product was obtained by removing the volatiles under reduced pressure. Product 5 was purified by flash column chromatography with hexane / ethyl acetate 3/1 to 1/1 gradient (0.65 g, 65% yield for 2 steps). 1H NMR (400 MHz, Chloroform-d) d 5.58 (d, J = 8.3 Hz, 1H), 5.07 (t, J = 9.5 Hz, 1H), 4.77 (t, J = 9.6 Hz, 1H), 3.76 – 3.60 (m, 2H), 3.05 (s, 1H), 2.15 (s, 3H), 2.07 (s, 5H), 2.04 (s, 4H), 1.20 (d, J = 6.2 Hz, 3H). MS (ESI) calculated mass for the parent C12H18O8290.10 [M], found 313.00 [M+Na]. (3S,4R,5S,6S)-6-methyl-3-(((trifluoromethyl)sulfonyl)oxy)tet rahydro-2H-pyran-2,4,5-triyl triacetate The triacetate 5 (0.52 g, 1.79 mmol) was dissolved in anhydrous CH ₂ Cl ₂ (20 mL) and anhydrous pyridine (1.2 mL) and cooled with ice-salt bath. Trifluoromethanesulfonic anhydride (1.52 g, 5.37 mmol) in CH ₂ Cl ₂ (10 mL) was added dropwise. The mixture was stirred under room temperature for 20 minutes, sequentially washed with HCl (0.3 M, 30 mL), saturated NaHCO3 (30 mL) and brine (30 mL). The organic layer was dried over anhydrous Na ₂ SO ₄ . Crude product was obtained by removing the volatiles under reduced pressure. Flash column chromatography was used to purify the product 6 with hexane / ethyl acetate 3/1 to 1/1 gradient (0.75 g, quant. yield). 1H NMR (400 MHz, Chloroform-d) d 5.80 (d, J = 8.3 Hz, 1H), 5.38 (t, J = 9.6 Hz, 1H), 4.89 – 4.76 (m, 2H), 3.78 (dq, J = 9.7, 6.1 Hz, 1H), 2.16 (s, 3H), 2.07 (s, 3H), 2.05 (s, 3H), 1.25 (d, J = 6.2 Hz, 3H). ¹³ C NMR (101 MHz, CDCl3) d 169.53, 169.51, 168.44, 118.21 (q, J = 319.0 Hz), 90.21, 80.92, 77.35, 77.23, 77.03, 76.71, 73.02, 71.27, 71.24, 20.49, 20.37, 20.26, 17.02. MS (ESI) calculated mass for the parent C13H17F3O10S 422.05 [M], found 362.90 [M-OAc]. (3R,4R,5S,6S)-3-fluoro-6-methyltetrahydro-2H-pyran-2,4,5-tri yl triacetate To a solution of triflate 6 (50 mg, 0.118 mmol) in anhydrous acetonitrile (2 mL) was added TBAF in THF (1.0 M, 0.177 mL, 0.177 mmol). The solution was stirred under 65 °C overnight. The volatiles were removed under reduced pressure. Flash column chromatography was used to purify the product 7 with hexane / ethyl acetate 5/1 to 2/1 gradient (3.5 mg, 10% yield, a : b anomer ratio = 1 : 1). The product characterization was identical with the literature. 1H NMR (400 MHz, Chloroform-d) d 6.02 (s, 1H), 5.78 (d, J = 60 Hz, 1H), 5.35 – 5.30 (m, 1 H), 3.30-5.25 (m, 1H), 5.18 – 5.10 (m, 2H), 5.08 – 4.95 (m, 1H), 4.88 (dd, J = 120, 4.0 Hz, 1H), 4.00 – 3.80 (m, 1H), 3.73 – 3.65 (m, 1H), 2.20 (s, 3H), 2.09 (s, 3H), 2.08 (s, 3H), 2.12 (s, 3H), 2.08 (s, 3H), 2.02 (s, 3H), 1.30 (d, J = 6.0 Hz, 3H), 1.25 (d, J = 6.0 Hz, 3H). MS (ESI) calculated mass for the parent C ₁₂ H ₁₇ FO ₇ 292.10 [M], found 273.10 [M-F]. (3R,4R,5R,6S)-3-fluoro-6-methyltetrahydro-2H-pyran-2,4,5-tri ol (2-deoxy-2-fluororhamnose) Triacetate 7 (3.5 mg, 0.012 mmol) was dissolved in TFA (1.0 mL) and stirred under 50 °C for 1 hour. The volatiles were removed under reduced pressure to yield 2-deoxy-2-fluororhamnose as a yellow oil (1.2 mg). ¹⁹ F NMR chromatogram was compared with literature which found identical result. (Liu et al., Chem. Eur. J.2016, 22 , 12557-12565.) Example 2 Radiosynthesis of 2-deoxy-2-[ ¹⁸ F]fluororhamnose Radiosynthesis of 2-deoxy-2-[ ¹⁸ F]fluororhamnose was performed on a GE Tracerlab FX-N2 synthesizer. The synthesis comprised 9 reagent vials on the GE synthesizer. Vials 1-5 were used for the elution, drying of F-18, and fluorination reaction. Vials 13–14 were used for the formulation of purified intermediate, and vials 9–10 for the hydrolysis and formulation of final product [ ¹⁸ F]9. Specifically, Vial 1 was added with tetrabutylammonium bicarbonate solution (150 µL, 0.075M), 50 µL water and MeOH (1 mL); Vial 2 was added with acetonitrile (ACN) (1 mL); Vial 3 was added with the tosylate precursor 2 (5 mg) in ACN (0.6 mL); Vial 4 was added with water (0.5 mL); Vial 4 was added with 1 mL water; Vial 5 was added with HPLC solvent (2.0 mL, 40% ACN in 0.1% trifluoroacetic acid (TFA)); Vial 9 was added with HCl (1N, 700 µL); Vial 10 was added with NaOH (1N, 500 µL); Vial 13 was added with EtOH (1.2 mL); Vial 14 was added with water (6 mL); HPLC dilution flask was added with water (30 mL). Vial 11 inlet port was connected with valve 15 (V15) right port for transferring intermediate to reaction vial 2 (RV2). Typically, 7.4 GBq (200 mCi) [ ¹⁸ F]fluoride in 2.5 mL of water was passed through a PS- HCO3 cartridge, which was rinsed with 1 mL of acetonitrile. [ ¹⁸ F]fluoride was eluted from the cartridge into reactor 1 (R1) with the eluent in Vial 1, and dried under N ₂ /vacuum at 75 °C for 4 minutes. R1 was cooled to 50 °C, acetonitrile in Vial 2 was added and the activity was azeotropically dried at 55 °C for 3 minutes and at 95 °C for 3 minutes under N ₂ /vacuum. The activity was further dried using a vacuum for 3 minutes. The [ ¹⁸ F]fluoride drying cycle took about 20 minutes. The tosylate precursor solution in Vial 3 was added to the dried activity. The resulting solution was stirred at 70 °C for 20 minutes, then cooled to 45 °C. The reaction mixture was diluted with 1.0 mL of water (Vial 4), and transferred in Tube 2. R1 was rinsed with HPLC mobile phase (Vial 5) and the solution was also transferred to Tube 2. The solution in Tube 2 was thoroughly mixed by bubbling N ₂ for 10 seconds and injected into the HPLC for purification. HPLC condition: Phenomenex Luna (2) C18 column, 250 × 10 mm, 5 µm. Mobile phase: 40% ACN in 0.1% TFA. Flow rate: 4 mL/min. The labeled intermediate was eluted at about 12–14 minutes. The intermediate was collected in the dilution flask containing 30 mL water, and passed through an Oasis HLB plus cartridge (pre-conditioned with 5 mL of ethanol, 10 mL of air, and 10 mL of water). The trapped intermediate was rinsed with 6 mL water (Vial 14), and eluted with 1.2 mL of absolute ethanol (Vial 13) to R2 through value 35 (V35). The eluted intermediate was heated to 60 °C under N2 flow and vacuum for 3 minutes to remove ethanol. NaOH in Vial 10 was added to the dried residue. The resulting solution was heated at 45 °C for 10 minutes. HCl solution in Vial 9 was added, the content was transferred through V16 and an in-line sterile filter to the product vial. The product was analyzed by HPLC. HPLC conditions: Waters BEH Amide column (150*4.6 mm), 3.5 µm. Using 90% -50% D in 8 minutes. C: 95% water + 5% ACN with 0.1% NH ₄ OH; D: 95% ACN + 5% water with 0.1% NH4OH. The product peak eluted at about 4 minutes. Generally, 2-deoxy-2-[ ¹⁸ F]fluororhamnose 9 was synthesized in 7-12% radiochemical yield (uncorrected, n > 5), radiochemical purity >95%. The synthesis time was about 90 minutes. A manual method also was used to produce the radiolabeled product. Different bases were tried and produced various overall yields.

Example 3 Synthesis of 6-F-Rhamnose (3S,5S,6R)-6-((trityloxy)methyl)tetrahydro-2H-pyran-2,3,4,5- tetrayl tetraacetate Triphenylmethyl chloride (3.4 g, 12.2 mmol) was added to L-Mannose 10 (2.00 g, 11.1 mmol) in anhydrous pyridine (10 mL). The mixture was stirred at room temperature for 15 hours. 6 mL of Ac2O was added afterwards and the solution was stirred for another 15 hours. The mixture was poured into ice-cold water and extracted with EtOAc (3 x 100 mL). The combined organic layer was washed with brine and dried over Na2SO4. After evaporation of solvents, the residue was purified by silica gel flash chromatography to afford the product 11 as a white solid (5.84 g, 89%). 1H NMR (400 MHz, CDCl3): d 7.46-7.22 (m, 15 H), 6.10 (s, 0.7H), 5.85 (s, 0.3H), 5.52 (m, 1H), 5.43-5.52 (m, 2H), 3.91 (m, 0.7H), 3.64 (m, 0.3H), 3.34 (m,1H), 3.18 (0.3H), 3.07 (m, 0.7H), 2.24 (s, 2.1H), 2.23 (s, 0.9H), 2.17 (s, 2.1H), 2.14 (s, 0.9H), 2.00 (s, 2.1H), 1.98 (s, 0.9H), 1.76 (s, 0.9H), 1.75 (s, 2.1H). (3S,5S,6R)-6-(hydroxymethyl)tetrahydro-2H-pyran-2,3,4,5-tetr ayl tetraacetate 33% HBr in HOAc (1.6 mL) was added to the solution of compound 11 (4.60 g, 7.80 mmol) in glacial acetic acid (16 mL) at 10 °C. The mixture was stirred for 10 minutes. The formed triphenylmethyl bromide was immediately removed by filtration. The filtrate was diluted with cold water and extracted with EtOAc (3 x 100 mL). The combined organic layer was washed with water, brine and dried over Na ₂ SO ₄ . After evaporation of solvents, the residue was purified by silica gel flash chromatography to afford the product 12 as a white solid (2.23 g, 82%). 1H NMR (400 MHz, CDCl ₃ ): d 6.09 (d, 0.67H, J = 1.6 Hz), 5.87 (d, 0.33 H, J = 1.2 Hz), 5.49 (dd, 0.33 H, J = 1.2 and 11.5 Hz), 5.40 (dd, 0.67 H, J = 3.3 and 10.0 Hz), 5.33 (m, 0.67H), 5.27 (m, 1H), 5.17 (dd, 0.33 H, J = 3.3 and 10.5 Hz), 3.85 (m, 0.67H), 3.73 (m, 1H), 3.66-3.58 (m, 1.33H), 2.21 (s, 0.99H), 2.17 (s, 2.01H), 2.16 (s, 2.01H), 2.10 (s, 0.99H), 2.08 (s, 2.01H), 2.04 (s, 0.99H), 2.02 (s, 2.01H), 2.01 (s, 0.99H). 3S,5S,6R)-6-((((trifluoromethyl)sulfonyl)oxy)methyl)tetrahyd ro-2H-pyran-2,3,4,5-tetrayl tetraacetate Trifluoromethanesulfonic anhydride (0.37 mL, 2.2 mmol) was added to a mixture of compound 12 (696 mg, 2.0 mmol) and pyridine (0.25 mL) in dichloromethane (20 mL) at -10 °C. After stirring for 2 hours, water (50 mL) was added. The organic layer was separated and the aqueous layer was extracted with dichloromethane (3 x 50 mL). The organic layers were combined, washed with 10% H ₂ SO ₄ , sat. NaHCO ₃ , brine and dried over MgSO ₄ . After evaporation of solvents, the residue was purified by silica gel flash chromatography to afford the product 13 as a white solid (826 mg, 86%). 1H NMR (400 MHz, CDCl3): d 6.12 (d, 0.62H, J = 2.0 Hz), 5.89 (d, 0.38 H, J = 1.2 Hz), 5.49 (dd, 0.38 H, J = 1.2 and 3.1 Hz), 5.39 (dd, 0.62 H, J = 3.1 and 10.2 Hz), 5.33 (m, 0.62H), 5.30 (m, 0.38H), 5.26 (dd, 0.62H, J = 1.2 and 11.5 Hz), 5.16 (dd, 0.38 H, J = 3.1 and 9.8 Hz), 4.58-4.54 (m, 2H), 4.14 (m, 0.62H), 3.92 (m, 0.38), 2.22 (s, 1.14H), 2.19 (s, 1.86Hx2), 2.12 (s, 1.14H), 2.10 (s, 1.86H), 2.05 (s, 1.14H), 2.03 (s, 1.86H), 2.02 (s, 1.14H). ¹⁹ F NMR (376 MHz, CDCl3): d -74.3, - 74.4. (3S,4R,5R,6R)-6-(fluoromethyl)tetrahydro-2H-pyran-2,3,4,5-te trayl tetraacetate DAST (0.30 mL, 2.27 mmol) was slowly added to a solution of 13 (104 mg, 0.30 mmol) in anhydrous CH ₂ Cl2 (5 mL) at -40 °C. The reaction was stirred at room temperature for 24 hours. After cooled down to -20 °C, MeOH (1 mL) was added and the solvent was removed under reduced pressure. The residue was diluted with CH ₂ Cl2 (75 mL), washed with water and dried over MgSO4. After evaporation of solvents, the residue was purified by silica gel flash chromatography to afford the product 14 as a colorless oil (30 mg, 28%). ¹⁹ F NMR (376 MHz, CDCl3): d -231.9, -232.4. (3S,4R,5R,6R)-6-(fluoromethyl)tetrahydro-2H-pyran-2,3,4,5-te traol NaOMe (13.5 mg, 0.25 mmol) was added to a suspension of 14 (22 mg, 0.063 mmol) in dry MeOH (3 mL). The mixture was stirred at room temperature for 15 hours. Then the reaction mixture was neutralized with Dowex (H+) resin, filtrated, concentrated and purified by silica gel flash column chromatography to afford 15 as a white solid (10 mg, 87%). 1H NMR (400 MHz, D2O/CD3OD): d 5.18 (d, 0.6H, J = 2.0 Hz), 4.92 (d, 0.4 H, J = 1.2 Hz), 4.78-4.57 (m, 2H), 3.93 (m, 1H), 3.87 (m, 1H), 3.77 (m, 1H), 3.68 (m, 1H). Example 4 Radiosynthesis of 6-[ ¹⁸ F]fluororhamnose Radiosynthesis of 6-[ ¹⁸ F]fluororhamnose was performed on a GE Tracerlab FX-N2 synthesizer. The synthesis comprised 9 reagent vials on the GE synthesizer. Vials 1-5 were used for the elution, drying of F-18, and fluorination reaction. Vials 13–14 were used for the formulation of purified intermediate, and vials 9–10 for the hydrolysis and formulation of final product [ ¹⁸ F]16. Specifically, Vial 1 was added with tetrabutylammonium bicarbonate solution (150 µL, 0.075M), 50 µL water and MeOH (1 mL); Vial 2 was added with ACN (1 mL); Vial 3 was added with the tosylate precursor 2 (5 mg) in ACN (0.6 mL); Vial 4 was added with water (0.5 mL); Vial 4 was added with 1 mL water; Vial 5 was added with HPLC solvent (2.0 mL, 40% ACN in 0.1% TFA); Vial 9 was added with HCl (1N, 700 µL); Vial 10 was added with NaOH (1N, 500 µL); Vial 13 was added with EtOH (1.0 mL); Vial 14 was added with water (6 mL); HPLC dilution flask was added with water (30 mL). Vial 11 inlet port was connected with V15 right port for transferring intermediate to RV2. Typically, 7.4 GBq (200 mCi) [ ¹⁸ F]fluoride in 2.5 mL of water was passed through a PS- HCO ₃ cartridge, which was rinsed with 1 mL of acetonitrile. [ ¹⁸ F]fluoride was eluted from the cartridge into reactor 1 (R1) with the eluent in Vial 1, and dried under N2/vacuum at 75 °C for 4 minutes. R1 was cooled to 50 °C, acetonitrile in Vial 2 was added and the activity was azeotropically dried at 55 °C for 3 minutes and at 95 °C for 3 minutes under N2/vacuum. The activity was further dried using a vacuum for 3 minutes. The [ ¹⁸ F]fluoride drying cycle took about 20 minutes. The tosylate precursor solution in Vial 3 was added to the dried activity. The resulting solution was stirred at 70 °C for 20 minutes, cooled to 45 °C. The reaction mixture was diluted with 1.0 mL of water (Vial 4), and transferred in Tube 2. R1 was rinsed with HPLC mobile phase (Vial 5) and the solution was also transferred to Tube 2. The solution in Tube 2 was thoroughly mixed by bubbling N ₂ for 10 seconds and injected into the HPLC for purification. HPLC condition: Phenomenex Luna (2) C18 column, 250 × 10 mm, 5 µm. Mobile phase: 40% ACN in 0.1% TFA. Flow rate: 4 mL/min. The labeled intermediate was eluted at about 12–14 minutes. The intermediate was collected in the dilution flask containing 30 mL water, and passed through an Oasis HLB light cartridge (pre-conditioned with 5 mL of ethanol, 10 mL of air, and 10 mL of water). The trapped intermediate was rinsed with 6 mL water (Vial 14), and eluted with 1.0 mL of absolute ethanol (Vial 13) to R2 through V35. The eluted intermediate was heated to 60 °C under N ₂ flow and vacuum for 3 minutes to remove ethanol. NaOH in Vial 10 was added to the dried residue. The resulting solution was heated at 45 °C for 10 minutes. HCl solution in Vial 9 was added, the content was transferred through valve 16 (V16) and an in-line sterile filter to the product vial. The product was analyzed by HPLC: Waters BEH Amide column (150*4.6 mm), 3.5 µm. Using 90% -50% D in 8 min. C: 95% water + 5% ACN with 0.1% NH4OH; D: 95% ACN + 5% water with 0.1% NH4OH. The product peak eluted at about 5 minutes. Generally, 6-[18F]fluororhamnose was synthesized in 18- 25% radiochemical yield (uncorrected, n > 3), radiochemical purity >95%. The synthesis time was about 90 minutes. Example 5 Synthesis of 3-deoxy-3-F-Rhamnose (3R,4R,5S,6S)-4-(benzyloxy)-2-methoxy-6-methyltetrahydro-2H- pyran-3,5-diol Methyl-rhamnopyranoside 17 (2.85 g, 16.0 mmol), benzyl bromide (2.91 mL, 24 mmol), dimethyltin dichloride (351 mg, 1.6 mmol) and Ag2O (4.07 g, 17.6 mmol) were stirred in anhydrous acetonitrile (90 mL) at room temperature for 15 hours. After filtered through a celite pad, the filtrate was evaporated and the residue was purified by silica gel flash chromatography to afford 18 as a colorless oil (3.41 g, 79%, a:b = 1). b-isomer: ¹ H NMR (400 MHz, CDCl3) d 7.30-7.32 (m, 5H), 4.71 (d, 1H, J = 1.6 Hz), 4.70 (d, 1H, J = 11.3 Hz), 4.57 (d, 1H, J = 11.3 Hz), 4.02 (dd, 1 H, J = 1.6 and 3.1 Hz), 3.67-3.61 (m, 2H), 3.56 (m, 1 H), 3.36 (s, 3H), 1.32 (d, J = 6.3 Hz, 3H). a-isomer: ¹ H NMR (400 MHz, CDCl ₃ ) d 7.39-7.32 (m, 5H), 4.75 (d, 1H, J = 11.3 Hz), 4.74 (s, 1H), 4.52 (d, 1H, J = 11.7 Hz), 3.72-3.68 (m, 2H), 3.60 (m, 1 H), 3.42 (t, 1H, J = 9.0 Hz), 3.35 (s, 3H), 1.34 (d, J = 6.3 Hz, 3H). (3R,4R,5S,6S)-4-(benzyloxy)-5-hydroxy-6-methyltetrahydro-2H- pyran-2,3-diyldiacetate Compound 18 (3.24 g, 12.1 mmol) was dissolved in anhydrous pyridine (12 mL) and Ac2O (7 mL). The solution was stirred at room temperature for 15 hours. Solvents were evaporated and the residue was dissolved in EtOAc (300 mL), washed with saturated NaHCO3, 1N HCl, H ₂ O, brine and dried over Na ₂ SO ₄ . After evaporation of solvents, the crude product 19 was used for next step. H ₂ SO4 (0.6 mL) was added dropwise to a solution of 19 (4.25 g, 12.1 mmol) in Ac2O (20 mL) and the solution was stirred at room temperature for 5 hours. The reaction mixture was poured into a stirred mixture of ethyl acetate (150 mL) and saturated NaHCO3 (80 mL). The organic phase was separated and washed with saturated NaHCO ₃ , brine and dried over Na ₂ SO ₄ . After evaporation of solvents, the residue was purified by silica gel flash chromatography to afford the product 20 as a colorless oil (3.37 g, 73%). ¹ H NMR (400 MHz, CDCl ₃ ): d 7.37-7.26 (m, 5H), 6.12 (d, 0.27H, J = 2.0 Hz ), 6.03 (d, 0.73H, J = 2.0 Hz), 5.34 (dd, 0.73H, J = 2.0 and 3.5 Hz), 5.23 (m, 0.27H), 5.16 (m, 0.27H), 5.07 (t, 0.73H, J = 9.0 Hz), 4.72-4.43 (m, 2H), 3.94-3.79 (m, 2H), 2.16 (s, 2.19H), 2.12 (s, 0.81H), 2.11 (s, 2.19H), 2.10 (s, 0.81H), 2.05 (s, 0.81H), 2.04 (s, 2.19H), 1.23 (d, J = 6.3 Hz, 0.81H), 1.21(d, J = 6.3 Hz, 2.19H). (3R,4R,5R,6S)-4-hydroxy-6-methyltetrahydro-2H-pyran-2,3,5-tr iyl triacetate 10% Pd/C (1.5 g) was added to 20 (3.15 g, 8.28 mmol) in EtOAc (200 mL). The mixture was stirred at room temperature under H ₂ atmosphere for 2 hours and filtered through a celite pad. The filtrate was evaporated and the residue was purified by silica gel flash chromatography to afford 21 as a white solid (2.14 g, 89%). 1H NMR (400 MHz, CDCl ₃ ): d 6.10 (d, 0.26H, J = 2.0 Hz ), 6.06 (d, 0.74H, J = 1.6 Hz), 5.25 (dd, 0.26H, J = 3.1 and 9.8 Hz), 5.17 (m, 0.26H), 5.09 (dd, 0.74H, J = 1.8 and 13.7 Hz), 4.90 (t, 0.74H, J = 9.8 Hz), 4.10-4.00 (m, 1H), 3.97-3.84 (m, 1H), 2.16 (s, 2.22H), 2.12 (s, 0.78H), 2.11 (s, 2.22H), 2.10 (s, 0.78H), 2.05 (s, 0.78H), 2.04 (s, 2.22H), 1.23 (d, J = 6.3 Hz, 0.78H), 1.21(d, J = 6.3 Hz, 2.22H). (3R,4R,5S,6S)-6-methyl-4-(((trifluoromethyl)sulfonyl)oxy)tet rahydro-2H-pyran-2,3,5-triyl triacetate Trifluoromethanesulfonic anhydride (0.33 mL, 1.94 mmol) was added to a mixture of compound 21 (508 mg, 1.75 mmol) and pyridine (0.22 mL) in dichloromethane (18 mL) at -18 ^o C. After stirring for 0.5 hours, the mixture was warmed up to room temperature and stirred for additional 0.5 hours. Water (50 mL) was added and the organic layer was separated. The aqueous layer was extracted with dichloromethane (3 x 50 mL). The combined organic layers were washed with 10% H ₂ SO4, saturated NaHCO3, brine and dried over MgSO4. After evaporation of solvents, the residue was purified by silica gel flash chromatography to afford the product 22 as a colorless oil (494 mg, 67%). 1H NMR (400 MHz, CDCl ₃ ): d 6.06 (d, 1H, J = 2.0 Hz), 5.38 (dd, 1H, J = 2.0 and 3.5 Hz), 5.28 (t, 1H, J = 9.8 Hz), 5.18 (dd, 1H, J = 3.7 and 10.0 Hz), 3.92 (m, 1H), 2.21 (s, 3H), 2.18 (s, 3H), 2.15 (s, 3H), 1.27 (d, J = 6.3 Hz, 3H). ¹⁹ F NMR (376 MHz, CDCl ₃ ): d -75.0. (3R,4S,5R,6S)-4-hydroxy-6-methyltetrahydro-2H-pyran-2,3,5-tr iyl triacetate Compound 22 (422 mg, 1.0 mmol) was dissolved in dry CH ₃ CN (2 mL) and solid tetrabutylammonium nitrite (1.44 g, 5 mmol) was added. After stirring for 1 hour at room temperature, the reaction mixture was evaporated. The residue was dissolved in CH ₂ Cl ₂ , washed with brine and dried over MgSO4. After evaporation of solvents, the residue was purified by silica gel flash chromatography to afford the product 23 as a white solid (87 mg, 30%). 1H NMR (400 MHz, CDCl3): d 5.95 (d, 0.84H, J = 2.3 Hz ), 5.91 (s, 0.16H), 5.10 (m, 0.16H), 5.02 (dd, 0.16H, J = 1.6 and 3.5 Hz), 5.00 (dd, 0.84H, J = 2.3 and 4.3 Hz), 4.89 (dd, 0.84H, J = 3.3 and 8.8 Hz), 4.27 (m, 0.84H), 4.12-4.06 (m, 1H), 3.74 (m, 0.16H), 2.15 (s, 0.48H), 2.13 (s, 0.84x6H), 2.12 (s, 0.84x3H), 2.11 (s, 0.48H), 2.10 (s, 0.48H), 1.33 (d, J = 6.7 Hz, 0.48H), 1.25(d, J = 6.7 Hz, 0.84x3H). (3R,4S,5S,6S)-6-methyl-4-(((trifluoromethyl)sulfonyl)oxy)tet rahydro-2H-pyran-2,3,5-triyl triacetate Compound 23 is treated with trifluoromethanesulfonic anhydride and pyridine to make compound 24 according to the method previously described with respect to the synthesis of compound 22. (3S,4R,5S,6S)-4-fluoro-6-methyltetrahydro-2H-pyran-2,3,5-tri yl triacetate Compound 24 is treated with DAST to make compound 25 according to the method previously described with respect to the synthesis of compound 14. (3S,4R,5S,6S)-4-fluoro-6-methyltetrahydro-2H-pyran-2,3,5-tri ol Compound 25 is treated with NaOMe to make compound 26 according to the method previously described with respect to the synthesis of compound 15. Example 6 Radiosynthesis of 3-deoxy-3-[ ¹⁸ F]-fluororhamnose 3-deoxy-3-[ ¹⁸ F]-fluororhamnose is synthesized from compound 24 using the method previously described, such as in Examples 2 and 4.

Example 7 Synthesis of (3R,4R,5S,6R)-5-(((2S,3R,4S,5S,6R)-3-[ ¹⁸ F]-fluoro-4,5-dihydroxy-6- (hydroxymethyl)tetrahydro-2H-pyran-2-yl)oxy)-6-(hydroxymethy l)tetrahydro-2H-pyran- 2,3,4-triol) (2R,3R,4S,5S,6S)-2-(Acetoxymethyl)-5-(benzyloxy)-6-(((1R,2R, 3S,4R)-3,4-diacetoxy-6,8- dioxabicyclo[3.2.1]octan-2-yl)oxy)tetrahydro-2H-pyran-3,4-di yl diacetate (29) A solution of compound 27 in anhydrous ether is added slowly to a stirred solution of compound 28 in anhydrous acetonitrile containing silver trifluoromethanesulfonate (CF ₃ SO ₃ Ag), silver carbonate (Ag2CO3) and powdered drierite. The resulting mixture is stirred at room temperature and filtered through celite. The residue is washed with CH ₂ Cl ₂ . The combined filtrates are evaporated and the residue is purified by silica gel flash chromatography to produce compound 29. (3R,4S,5R,6R)-6-(Acetoxymethyl)-5-(((2S,3S,4S,5R,6R)-4,5-dia cetoxy-6-(acetoxymethyl)-3- (benzyloxy)tetrahydro-2H-pyran-2-yl)oxy)tetrahydro-2H-pyran- 2,3,4-triyl triacetate (30) Compound 29 is treated with Ac ₂ O and H ₂ SO ₄ to make compound 30, using the method previously described in the synthesis of compound 20. (3R,4S,5R,6R)-6-(Acetoxymethyl)-5-(((2S,3S,4R,5R,6R)-4,5-dia cetoxy-6-(acetoxymethyl)-3- hydroxytetrahydro-2H-pyran-2-yl)oxy)tetrahydro-2H-pyran-2,3, 4-triyl triacetate (31) Compound 30 is treated with 10% Pd/C and H ₂ to make compound 31, using the method previously described in the synthesis of compound 21. (3R,4S,5R,6R)-6-(Acetoxymethyl)-5-(((2S,3S,4S,5R,6R)-4,5-dia cetoxy-6-(acetoxymethyl)-3- (((trifluoromethyl)sulfonyl)oxy)tetrahydro-2H-pyran-2-yl)oxy )tetrahydro-2H-pyran-2,3,4- triyl triacetate (32) Compound 31 is treated with trifluoromethanesulfonic anhydride and pyridine to make compound 32, using the method previously described in the synthesis of compound 22. (3R,4R,5S,6R)-5-(((2S,3R,4S,5S,6R)-3-Fluoro-4,5-dihydroxy-6- (hydroxymethyl)tetrahydro- 2H-pyran-2-yl)oxy)-6-(hydroxymethyl)tetrahydro-2H-pyran-2,3, 4-triol (33) n-Bu4NF is added to a solution of compound 32 in anhydrous acetonitrile. The reaction mixture is stirred at room temperature, concentrated and the residue is purified by flash chromatography on a silica gel column to give the intermediate product which is treated with NaOMe to produce compound 33, using the method previously described in the synthesis of compound 15. (3R,4R,5S,6R)-5-(((2S,3R,4S,5S,6R)-3-[ ¹⁸ F]-fluoro-4,5-dihydroxy-6- (hydroxymethyl)tetrahydro-2H-pyran-2-yl)oxy)-6-(hydroxymethy l)tetrahydro-2H-pyran- 2,3,4-triol (8-deoxy-8-[ ¹⁸ F]-fluorocellobiose) 8-deoxy-8-[ ¹⁸ F]-fluorocellobiose is synthesized from compound 32 using the methods described herein.

Example 8 Synthesis of (2S,3R,4S,5S,6R)-2-(((2R,3S,4S,5R,6R)-5-[ ¹⁸ F]-fluoro-4,6-dihydroxy-2- (hydroxymethyl)tetrahydro-2H-pyran-3-yl)oxy)-6-(hydroxymethy l)tetrahydro-2H-pyran- 3,4,5-triol) (3S,4S,5R,6R)-6-(Acetoxymethyl)-5-(((2S,3R,4S,5R,6R)-3,4,5-t riacetoxy-6-(acetoxymethyl) tetrahydro-2H-pyran-2-yl)oxy)tetrahydro-2H-pyran-2,3,4-triyl triacetate (35) Compound 34 is treated with Ac2O and pyridine to make compound 35, using the method previously described in the synthesis of compound 19. (2R,3R,4S,5R,6S)-2-(Acetoxymethyl)-6-(((2R,3R,4S,5S,6R)-4,5- diacetoxy-2-(acetoxymethyl) - 6-iodotetrahydro-2H-pyran-3-yl)oxy)tetrahydro-2H-pyran-3,4,5 -triyl triacetate (36) Iodine and triethylsilane are sequentially added to a solution of compound 35 in dichloromethane. The reaction is stirred at reflux temperature until TLC analysis indicates that the reaction is substantially complete. After cooling to room temperature, the mixture is diluted with dichloromethane and washed with a solution of saturated sodium hydrogen carbonate containing sodium thiosulfate for reducing the residual amount of iodine. The aqueous phase is extracted with dichloromethane, and the collected organic phase is dried with sodium sulfate and concentrated to provide the crude product 36 for next step. (2S,3R,4S,5R,6R)-2-(((3aS,5R,6R,7S,7aS)-7-Acetoxy-5-(acetoxy methyl)-2-(benzyloxy)-2- methyltetrahydro-5H-[1,3]dioxolo[4,5-b]pyran-6-yl)oxy)-6-(ac etoxymethyl)tetrahydro-2H- pyran-3,4,5-triyl triacetate (37) Freshly activated 4 Å molecular sieves are added to the residue, and the mixture is suspended in anhydrous dichloromethane. 2,4,6-collidine and BnOH are then added, and the mixture is stirred at room temperature. The mixture is filtered through a short pad of silica gel, and the residue from the filtered liquor is purified by silica gel flash chromatography to afford the product 37. (2R,3R,4S,5R,6S)-2-(Acetoxymethyl)-6-(((2R,3R,4R,5S,6S)-4,6- diacetoxy-2-(acetoxymethyl) - 5-hydroxytetrahydro-2H-pyran-3-yl)oxy)tetrahydro-2H-pyran-3, 4,5-triyl triacetate (38) Compound 37 is treated with 10% Pd/C and H ₂ to make compound 38, using the method previously described in the synthesis of compound 21. (2R,3R,4S,5R,6S)-2-(Acetoxymethyl)-6-(((2R,3R,4S,5S,6S)-4,6- diacetoxy-2-(acetoxymethyl) - 5-(((trifluoromethyl)sulfonyl)oxy)tetrahydro-2H-pyran-3-yl)o xy)tetrahydro-2H-pyran-3,4,5- triyl triacetate (39) Compound 38 is treated with trifluoromethanesulfonic anhydride and pyridine to make compound 39, using the method previously described in the synthesis of compound 22. (2R,3R,4S,5R,6S)-2-(Acetoxymethyl)-6-(((2R,3R,4S,5R,6S)-4,6- diacetoxy-2-(acetoxymethyl) - 5-fluorotetrahydro-2H-pyran-3-yl)oxy)tetrahydro-2H-pyran-3,4 ,5-triyl triacetate (40) Compound 39 is treated with n-Bu ₄ NF to make compound 40, using the method previously described in the synthesis of compound 33. (2S,3R,4S,5S,6R)-2-(((2R,3S,4S,5R,6R)-5-Fluoro-4,6-dihydroxy -2-(hydroxymethyl) tetrahydro-2H-pyran-3-yl)oxy)-6-(hydroxymethyl)tetrahydro-2H -pyran-3,4,5-triol (41) Compound 40 is treated with NaOMe to make compound 41 using the method previously described in the synthesis of compound 15. (2S,3R,4S,5S,6R)-2-(((2R,3S,4S,5R,6R)-5-[ ¹⁸ F]-fluoro-4,6-dihydroxy-2- (hydroxymethyl)tetrahydro-2H-pyran-3-yl)oxy)-6-(hydroxymethy l)tetrahydro-2H-pyran- 3,4,5-triol (2-deoxy-2-[ ¹⁸ F]-fluorocellobiose) 2-deoxy-2-[ ¹⁸ F]-fluorocellobiose is synthesized from compound 39 using the methods described herein. Example 9 L-Rhamnose as a Marker for Fungal Infection L-Rhamnose uptake is low in bacteria (gram negative and gram positive) and very low in P. aeruginosa and macrophages (Ordonez et al., J Nucl Med, 58: 144-50, 2017). L-Rhamnose is metabolized in Aspergillus species by alpha-rhamnosidases. Fungi such as Aspergillus use a nonphosphorylative pathway where L-Rhamnose is first oxidized to L-rhamno-g-lactone by L- rhamnose-1-dehydrogenase (LRA1). This intermediate is then converted to L-rhamnonate by L- rhamnono-g-lactonase (LRA2) and subsequently to L-2-keto-3-deoxyrhamnonate by L-rhamnonate dehydratase (LRA3). This is then cleaved into pyruvate and L-lactaldehyde by L-2-keto-3- deoxyrhamnonate (Watanabe et al., Febs J, 275:5139-49, 2008; Watanabe et al., J Biol Chem, 283:20372-82, 2008). Radiolabeled L-Rhamnose was tested as a fungal-specific ligand. In vitro uptake assays using 3H-L-Rhamnose (in vitro incubation of ³ H-L-Rhamnose with different cultures of Aspergillus, Rhizomucor, Cryptococcus, bacteria and macrophages followed by culture washing and measurement of retained radioactivity) showed significant retention of the sugar by A. fumigatus (FIG.1A), while minimal retention was seen with bacteria and macrophages (FIGS.1B- 1D). ex vivo experiments were performed, including biodistribution (injecting the animals with radiolabeled molecules followed by euthanasia, collection of organs and measurement of radioactivity) and autoradiography (sectioning of lung tissues from injected animals to measure residual radioactivity). Biodistribution studies showed uptake of ³ H-L-Rhamnose in the lungs of infected animals but not in uninfected controls (FIG.2). Autoradiography showed accumulation of ³ H-L-Rhamnose in the lungs of infected but not uninfected animals (FIG.1F). 1 ⁸ F-L-rhamnose PET ligand ( ¹⁸ F-2-deoxy-2-fluoro-L-hamnose; radiosynthesis details provided separately by the CSC) was synthesized as described in Examples 1 and 2, and evaluated for in vitro uptake by A. fumigatus and E. coli. ¹⁸ F-L-rhamnose was specifically internalized by live A. fumigatus cultures when compared to heat-killed cultures but not by E. coli. in vivo uptake of ¹⁸ F-L-rhamnose was assessed by PET/CT in mouse models of pulmonary aspergillosis (2 days following post-pharyngeal inoculation with Aspergillus cultures). Standardized uptake values (SUVs) of ¹⁸ F-L-rhamnose in infected mice were then measured, and compared to animals with sterile lung inflammation (24 hours following post-pharyngeal poly (I:C) administration) and healthy controls. In vivo PET/CT imaging with a 60-minute dynamic ¹⁸ F-L-rhamnose PET/CT imaging of a pulmonary aspergillosis model showed a slight higher uptake in lung lesions compared to controls and poly (I:C) treated mice (FIG.3A). There was however relatively fast washout of the ligand (FIG.3B). These results demonstrate that A. fumigatus selectively accumulates ¹⁸ F-L-rhamnose in vitro and in vivo. Based on these observations, ¹⁸ F-L-rhamnose derivatives with the ¹⁸ F located on other carbon atoms instead of C2, for example, C3 or C6, can be generated as described herein. These resulting ¹⁸ F-L-rhamnose derivatives (see Examples, 3-6) can be used to detect fungi in vivo or ex vivo using the methods provided herein. For example, dynamic PET/CT imaging and delayed PET/CT imaging (acquiring 60 minutes of dynamic data after injection of the ligand, and static imaging at 120 minutes post injection) can be performed. Bolus/infusion can be used to prolong the biological half-life of the compound and increase circulation time which would result in higher uptake by the fungi. Example 10 Cellobiose as a Marker for Fungal Infection Cellobiose, a disaccharide (two b-glucose molecules with a 1 ^4 glycosidic bond), is metabolized by Aspergillus fumigatus b-glucosidase and has no known human metabolism. In the presence of b-glucosidase, cellobiose is metabolized into two glucose molecules resulting in uptake in the area of infection as well as release of glucose into the circulation resulting in brain uptake (cellobiose does not cross the blood brain barrier, BBB). Thus, cellobiose can be radiolabeled and used as a ligand for fungal detection. In vitro studies using ³ H-cellobiose were performed with measurement of retained radioactivity after incubation and washing of the cultures using a beta counter. A. fumigatus had high uptake of ³ H-cellobiose (> than 2-deoxyglucose uptake) in culture (FIG.4A) while mammalian cells did not (FIG.4B). This uptake of ³ H-cellobiose in A. fumigatus increased over time, especially at 120 minutes. In biodistribution studies using ³ H-cellobiose (animals injected with ³ H-cellobiose followed by euthanasia, collection of organs and measurement of radioactivity), increased uptake in A. fumigatus-infected lungs (nasopharyngeal model) was found, as compared to uninfected animals (FIG.4C). Uptake in the brain was also noted in nasopharyngeally infected animals indicating hydrolysis of ³ H-cellobiose into two glucose molecules and secondary uptake of glucose molecules by brain cells. Uptake of ³ H-cellobiose by the infected animal lungs (nasopharyngeal inoculation model) and brains (intravenous inoculation model), but not in control animals or animals with sterile lung inflammation by autoradiography (sectioning of lung tissues from injected animals to measure retained radioactivity), was observed (FIGS.5A and 5B). Those findings were supported by GMS staining showing fungal hyphae in similar distributions to autoradiography uptake. To demonstrate the specificity of ³ H-cellobiose, in vitro screening of various bacteria can be performed with radioTLC to confirm the presence or lack of cellobiose metabolism. RadioTLC can be performed using ³ H-cellbiose as a reference and the presence of labeled glucose in the cell lysate obtained following incubation with fungi or bacteria can then be determined. If the pathogen has b-glucosidase, more than one peak will be detected, indicating metabolism (glucose and downstream metabolites); if the pathogen does not have b-glucosidase, only one peak representing the parent molecule (cellobiose), is detected. Radio-TLC can be used to evaluate plasma from control mice to further confirm the lack of mammalian metabolism for cellobiose: if b-glucosidase is expressed in the mouse, more than one peak will be detected, indicating metabolism (glucose and downstream metabolites) but if the enzyme is not present, as expected, only radiolabeled cellobiose will be detected. Radiosynthesis of labeled cellobiose can be achieved with ¹⁸ F located on one of the carbon atoms on the cellobiose molecule, for example, on C2 in the first or second glucose molecule (FIG. 6; see Examples 7 and 8). The in vitro uptake of both ¹⁸ F-cellobiose molecules can be measured as described herein and used for in vivo PET imaging as described herein. Since the resulting molecule is essentially FDG (after breaking the 1 ^4 glycosidic bond by b-glucosidase), this will result in uptake, phosphorylation and entrapment of ¹⁸ F-cellobiose metabolites in areas with fungal infection. In view of the many possible embodiments to which the principles of the disclosure may be applied, it should be recognized that the illustrated embodiments are only examples of the invention and should not be taken as limiting the scope of the invention. Rather, the scope of the invention is defined by the following claims. We therefore claim as our invention all that comes within the scope and spirit of these claims.