Method of measuring a deviation of an actual shape from a target shape of an optical surface

Field of the invention

The present invention relates to a method and a diffractive optical element for measuring a deviation of an actual shape from a target shape of an optical surface of a test object. Further, the invention relates to a measuring apparateus comprising such a diffractive optical element and an object having an aspherical optical surface.

Background of the invention

An optical surface to be measured can be the surface of an optical lens element or an optical mirror used in optical systems. Such optical systems can, for example, be configured as telescopes used in astronomy and systems used for imaging structures, such a structures formed on a mask or a reticule, onto a radiation sensitive substrate, such as resist, by a lithographic method. The quality of such optical systems is substantially determined by the accuracy with which the optical surface can be machined or manufactured to have a target shape determined by a designer of the optical system. In such manufacturing it is necessary to compare the actual shape of the machined optical surface with its target shape and to determine differences between the machined and the target surfaces. The optical surface may then be further machined especially at those portions where differences between the machined and the target surfaces exceed, for example, predefined thresholds.

lnterferometric measuring apparatuses are commonly used for high precision measurements of optical surfaces. An interferometric measuring apparatus for measuring an optical surface typically includes a source of sufficiently coherent

light and interferometer optics for generating a test wave incident on the surface to be tested, such that wave fronts of the test wave have, at a position of the surface to be tested, the same shape as the target shape of the surface under test. In such a situation, the test wave is orthogonally incident on the surface under test and is reflected therefrom to travel back towards the interferometer optics. Thereafter, the light of the test wave reflected from the surface under test is superimposed with light reflected from a reference surface and deviations between the shape of the surface under test and its target shape are determined from a resulting interference pattern.

While spherical wave fronts for testing spherical optical surfaces may be generated with relatively high precision by conventional interferometer optics, more advanced optics, such as computer generated holograms (CGHs) are mostly necessary to generate beams of measuring light having an aspherical wave front such that the light is orthogonally incident at each location of an aspherical surface under test.

The measurement data of optical surfaces are often negatively affected by disturbances which reduces the precision with which an asphere or a sphere can be manufactured. In case of rotationally symmetric spheres or aspheres non- rotationally symmetric disturbances, which are distant from the rotational axis, can be corrected by means of turn averaging methods. However, ring-like disturbances or disturbances on the rotational axis cannot be corrected. In the case of a free form surface having no axis of symmetry any disturbance reduces the accuracy of the measurement.

Summary of the invention

It is an object of the invention to solve the above-mentioned problems and in particular to provide a method and a diffractive optical element of the above type,

by means of which a deviation of an actual shape from a target shape of an optical surface can be measured at a higher level of accuracy.

This object is solved according to the invention by a method of measuring a deviation of an actual shape from a target shape of an optical surface of a test object, wherein the target shape is symmetrical about a rotational axis. The optical surface comprises an apex being traversed by the rotational axis and a subarea of the optical surface includes the apex. The method according to the invention comprises the steps of: generating an incoming light wave; diffracting the incoming light wave at a diffractive surface of a diffractive optical element and thereby generating a test wave having a wave front in the shape of the target shape, wherein the test wave is incident on the optical surface in autocollimation such that the test wave covers the apex of the optical surface and each single ray of the test wave being incident on the subarea of the optical surface is tilted with respect to a surface normal of the diffractive surface when emanating from the diffractive element; and interferometrically measuring a wave front of the test wave having interacted with the optical surface.

The object is further solved according to the invention by a method of measuring a deviation of an actual shape from a target shape of an optical surface of a test object which target shape has no axis of symmetry, which method comprises the steps of: generating an incoming light wave; diffracting the incoming light wave at a diffractive surface of a diffractive optical element and thereby generating a test wave having a wave front in the shape of the target shape, wherein each single ray of the test wave is tilted with respect to a surface normal of the diffractive surface when emanating from the diffractive element and the test wave is incident on the test surface in autocollimation; and interferometrically measuring a wave front of the test wave having interacted with the optical surface.

The object is further solved according to the invention by a diffractive optical element for measuring a deviation of an actual shape from a target shape of an optical surface of a test object, which target shape is symmetrical about a

rotational axis and comprises an apex being traversed by the rotational axis. The diffractive optical element according to the invention comprises a diffractive surface, which is adapted for diffracting the incoming light wave and thereby generating a test wave having a wave front in the shape of the target shape. The test wave is incident on the optical surface in autocollimation such that the test wave covers the apex of the optical surface and each single ray of which test wave being incident on the subarea of the optical surface is tilted with respect to a surface of the diffractive surface when emanating from the diffractive optical element.

The object is further solved according to the invention by a diffractive optical element for measuring a deviation of an actual shape from a target shape of an optical surface of a test object, which target shape has no axis of symmetry. The diffractive optical element according to the invention comprises a diffractive surface which is adapted for diffracting the incoming light wave and thereby generating a test wave. The test wave has a wave front in the shape of the target shape such that each single ray of the test wave is tilted with respect to a surface normal of the diffractive surface when emanating from the diffractive element and the test wave is incident on the optical surface in autocollimation.

The above object is further solved by a measuring apparatus for measuring a deviation of an actual shape from a target shape of an optical surface of a test object which measuring apparatus comprises: a light source for generating an incoming light wave, a diffractive optical element of the above type and an interferometer for measuring a wave front of the test wave having interacted with the optical surface.

The incoming light wave diffracted at the diffractive surface of the diffractive optical element according to the invention can, for example, be a plane wave or have another predefined wave front, for example, a spherical wave front. The incoming light wave needs to be sufficiently coherent to perform the respective interferometric measurement. As mentioned above, the test wave is incident on

the optical surface in autocollimation, therefore the test wave hits the optical surface such that each ray of the test wave is perpendicularly incident on a respective location of the optical surface. This way the test wave propagates back within itself in reflection.

In other words, according to the invention, the diffractive optical element is either adapted for testing an optical surface having a target shape which is symmetrical about a rotational axis or for testing an optical surface which target shape has no axis of symmetry. The wave front of the test wave generated by the diffractive optical element according to the invention is therfore shaped accordingly, as already mentioned above.

In the case in which the target shape is symmetrical about a rotational axis a portion of the optical surface, which includes an apex of the optical surface is referred to as subarea. The apex of the optical surface is the location of the optical surface being traversed by the rotational axis. According to the invention each single ray of the test wave, which is incident on the subarea of the optical surface, is tilted with respect to a surface normal of the diffractive surface when emanating from the diffractive element. Advantageously, the diffractive surface is a plane surface. In this case the surface normal of the diffractive surface is oriented the same at each location of the diffractive surface. In other words, according to the invention, no single ray of the test wave is perpendicular to the diffractive surface in the subarea when emanating from the diffractive element.

In the case, in which the target shape has no axis of symmetry and the optical surface is therefore a so-called "free form surface", according to the invention, each single ray of the test wave being incident on the entire optical surface is tilted with respect to a surface normal of the diffractive surface when emanating from the diffractive element.

The surface measurements obtained according to the invention show a significantly reduced amount of disturbances which improves the measurement

accuracy accordingly. The invention is based on the insight that the measure of having the single rays of the test wave tilted with respect to the surface normal of the diffractive surface reduces or completely eliminates the occurrence of reflexes in the second diffraction order of the incoming light wave at the diffractive surface. The reduction or complete elimination of the reflexes in the second diffractive order reduces the disturbances in the measurement data significantly which leads to an improved measurement accuracy of the actual shape of the optical surface.

In the case, in which the target shape of the optical surface is symmetrical about the rotational axis, for example is a rotationally symmetric sphere or asphere, second order reflections or Littrow-reflexes are avoided on the axis of the optical surface according to the invention. Reflexes of the incoming wave on an off-axis location of the diffractive optical element, i.e. on a location corresponding to a position outside of the subarea of the optical surface, also causes disturbances in the measurement. These disturbances, however, can be compensated for by rotating the test object around its rotational axis, taking a further measurement and stitching the measurement results. Such a compensation is known to the person skilled in the art as "turn-averaging". The compensation of the disturbance caused by a Littrow-reflex is made possible according to the inventive solution, as any Littrow-reflex still generated by the diffractive optical element is not rotationally symmetric, that means it is not at the apex of the optical surface and is no ring around the apex.

According to an embodiment of the invention the subarea is delimited by a circle around the apex having a radius of at least 5 mm projected onto the optical surface. Accordingly, reflexes of second order are suppressed in an area of 5 mm radius around the apex of the optical surface. In this way, disturbances in the measurement can be avoided particularly well.

In an embodiment of the method according to the invention for measuring an optical surface having a symmetrical target shape, the diffractive optical element is adapted such that each single ray of the test wave is tilted with respect to the

surface normal of the diffractive surface when emanating from the diffractive optical element. In this case, also off-axis reflections on the diffractive optical element are eliminated from the measurements.

In a further embodiment according to the invention the target shape of the optical surface is shaped as an asphere which deviates by more than 10 μm from its best fitting sphere. The rotational axis of the best fitting sphere corresponds preferably to the rotational axis of the target shape. An asphere having the above described deviation from its best fitting sphere can be measured particularly well by the method according to the invention.

In a further embodiment according to the invention the diffractive optical element is arranged such that the surface normal of the diffractive surface is tilted with respect to the rotational axis of the target shape by a tilt angle α. The tilt angle α is preferably at least 0.1 °, more preferably at least 1 °. This tilt angle has the effect of reducing second order reflections from the measurement data particularly well.

In a further embodiment according to the invention the diffractive optical element is tilted with respect to the optical surface such that a respective tangent plane of the optical surface is at no surface point within the subarea of the optical surface parallel to the diffractive surface. Such a tilt has the effect that the configuration of the diffractive optical element, which is adapted to the tilt, is such that no second order reflexes are generated from the incoming light wave in an on-axis area with respect to the optical surface to be tested.

In a further embodiment according to the invention the target shape of the optical surface is spherical.

In a further embodiment according to the invention the single rays of the test wave emanating from the diffractive optical element deviate from the surface normal of the diffractive surface by at least 0.1 °. The rays referred to here are either the single rays of the test wave being incident on the subarea in case of a

symmetrical target shape or each single ray incident upon the entire optical surface in case of the target shape having no axis of symmetry. A deviation of the single rays from the surface normal of the diffractive surface by at least 0.1 ° causes a large reduction of second order reflexes. Preferably the deviation is at least 1 ° which reduces the second order reflexes even more.

In a further embodiment according to the invention the diffractive element is tilted with respect to the optical surface such that the respective tangent plane of the optical surface is at no surface point parallel to the diffractive surface. As already explained above with respect to the embodiment, according to which no tangent plane of the optical surface within the subarea is parallel to the diffractive surface, the underlying tilt of the diffractive element reduces the amount of second order reflexes significantly.

In a further embodiment according to the invention the diffractive optical element is arranged such that the surface normal of the diffractive surface is tilted with respect to an average normal of the target shape. The average normal of the target shape is determined by averaging directions of the normals on the target shape on each location of the optical surface. As the wave front of the test wave has the shape of the target shape, the average normal of the target shape corresponds to an average propagation direction of the test wave. The tilt angle between the surface normal of the diffractive surface and the average normal of the target shape is preferably at least 0.1 °, most preferably at least 1 °. The average normal of the target shape also corresponds to the rotational axis of a rotationally symmetric optical surface.

In a further embodiment according to the invention an average propagation direction of the incoming light wave is tilted with respect to an average normal of the target shape. In this case the average propagation direction of the incoming light wave and an average propagation direction of the test wave are also tilted with respect to each other. The tilt angle is preferably at least 0.1 °, more preferably at least 1 °. Providing such a tilt angle between the average

propagation direction of the incoming light wave and the average normal of the target shape reduces disturbing reflexes, which are generated from light being transmitted by the diffractive optical element.

In a further embodiment according to the invention an average propagation direction of the test wave is tilted with respect to the surface normal of the diffractive surface by a tilt angle α. The tilt angle α is preferably at least 0.1 °, most preferably at least 1°. This tilt reduces the second order reflexes on the diffractive optical element further.

In a further embodiment according to the invention an average propagation direction of the incoming light wave is tilted with respect to the surface normal of the diffractive surface by a tilt angle β. The tilt angle β is preferably at least 0.1 °, more preferably at least 1 °. The tilt angle β reduces disturbing reflexes which are produced from the incoming light wave being transmitted by the diffractive optical element.

In a further embodiment according to the invention the surface normal of the diffractive surface is tilted with respect to an average propagation direction of the incoming light wave by a tilt angle β, wherein the tilt angle α between the average propagation direction of the test wave with respect to the surface normal is different from β. Preferably α differs from β by at least 0.1 °, more preferably by at least 1°. As mentioned above, the incoming light wave can, for example, be a spherical wave or a plane wave. In case the incoming light wave is a plane wave, its propagation direction is designated as the average propagation direction thereof. The embodiment according to which α ≠ β is particularly advantageous if the optical surface is a rotationally symmetric asphere, wherein α ≠ β avoids the line density of the diffractive structures from disappearing at the apex of the optical surface. In case α = β, the line density at the apex would be zero. As a line density of zero causes disturbances in the measurement of the optical surface, the measurement accuracy can be improved according to this embodiment.

In a further embodiment according to the invention no further optical element is arranged in the beam path of the test wave between the diffractive optical element and the optical surface. This way the measurement accuracy is improved even further as the wave front of the test wave is not distorted by optical inaccuracies of such an additional optical element.

In a further embodiment, the method according to the invention comprises the step of manufacturing the diffractive optical element prior to diffracting the incoming light wave, which manufacturing includes describing the phase function of the diffractive optical elements by means of splines. The phase function of the diffractive optical element is determined by means of splines such that the diffractive optical element produces the test wave having a wave front and respective propagation directions of its single rays to satisfy the conditions required by the above described method according to the invention. The description of the phase function by means of splines is performed as is known to the person skilled in the art by producing a two-dimensional polynomial representation such that a polynome is attributed to each cell. Other local polynomial description techniques can be used for describing the phase function as an alternative to the use of splines. According to a further embodiment the phase function of the diffractive optical element is described by means of a data grid, followed by an interpolation between the data points, which can be linear, quadratic or of higher order in order to determine the phase function of the diffractive optical element.

In a further embodiment according to the invention the interferometric measurement includes forming an interference pattern by superimposing the test wave having interacted with the optical surface and a reference wave, and the diffractive element is configured to compensate wave front errors introduced into the test wave due to a tilt of the surface normal of the diffractive surface with respect to a rotational axis of the target shape and/or to an average normal of the target shape. In particular, non-rotationally symmetric wave front errors are

compensated by the diffractive element. Advantageously, the maximum gradient of the test wave is smaller than 10, preferably smaller than 1 , and more preferably smaller than 0.1 fringes over the diameter of the optical surface projected into an interferometric camera. The interferometric camera is used for detecting the interference pattern formed by the test wave having interacted with the optical surface and the reference wave.

In a further embodiment according to the invention the diffractive optical element comprises a continuous substrate comprising the diffractive surface, which contains at least two diffractive structures, each of which is configured for diffracting the incoming light wave and thereby generating a respective test wave. The first diffractive structure is configured to generate from the incoming light wave a first test wave having a first wave front in the shape of a first target shape and a second diffractive structure is configured to generate from the incoming light wave a second test wave having a second wave front in the shape of a second target shape. According to this embodiment two differently shaped optical surfaces can be measured using the diffractive optical element with a high measurement accuracy. Further, the measurement of the two different optical surfaces can be performed in a time efficient manner as test waves for both optical surfaces can be generated from a single diffractive optical element. Use of a continuous substrate holding both diffractive structures has the further advantage that the diffractive optical element has to be aligned only once with respect to the diffractive surfaces to be tested. Further, a multitude of diffractive structures can be manufactured on a single continuous substrate much more cost efficiently than manufacturing the same number of diffractive optical elements each having only one diffractive structure. Advantageously, between 2 and 1000 diffractive structures each generating a differently shaped test wave from the incoming light wave are arranged on the single continuous substrate. According to further embodiments of the invention the diffractive structures are adapted for transforming the incoming light wave in the form of a plane wave or a spherical wave into the test wave which, for example, can be a spherical or an aspherical wave.

In a further embodiment according to the invention the average propagation directions of the different test waves are respectively tilted with respect to a surface normal of the substrate. In this way disturbances in the surface measurements can be reduced for each of the different optical surfaces measured. Advantageously the average propagation directions of the test waves are tilted with respect to the surface normal of the diffractive surface by at least 0.1 °, preferably at least 1°.

In a further embodiment according to the invention the diffractive optical element is movable from a first position to a second position with respect to the incoming light wave by rotation or translation of the diffractive optical element, in which first position the incoming light wave is incident on the first diffractive structure and the first test wave is generated, and in which second position the incoming light wave is incident on the second diffractive structure and the second test wave is generated, wherein the diffractive structures are configured such that the average propagation directions of the first and second waves are identical. This embodiment allows a subsequent measurement of differently shaped optical surfaces without the need to realign the diffractive optical element with respect to illumination means, which provide the input wave for each single measurement. According to the embodiment a first optical surface is tested with the optical element being in a first position. In this first position the incoming light wave is transformed by the first diffractive structure into the first test wave adapted for measuring a first optical surface. Subsequently, the diffractive optical element is moved such that the incoming light wave is now incident on a second diffractive structure. This move can be made either by rotating the diffractive optical element in a so-called "revolver" type arrangement or by translating the diffractive optical element accordingly. The second diffractive structure, which is now arranged in the beam path of the incoming light wave, transforms the incoming light wave into a second test wave adapted for testing a second optical surface. The second optical surface is arranged at the testing location at which the first optical surface was arranged before. No further adjustments are necessary as, according to the

embodiment, the average propagation direction of the second test wave is identical to the average propagation direction of the first test wave.

In a further embodiment according to the invention the diffractive structures extend over respective diffractive areas of the substrate, wherein each diffractive area has a respective center which is arranged within the respective diffractive area. The diffractive structures according to this embodiment are in particular not shaped as rings. Advantageously, the diffractive structures have similar sizes.

According to a further embodiment an average propagation direction of the incoming light wave is tilted with respect to the surface normal of the substrate. In this way disturbances in the measurement data due to reflexes from incoming light transmitted by the diffractive optical element can be reduced. Advantageously, the tilt of the average propagation direction of the incoming light wave with respect to the surface normal of the substrate is at least 0.1 °, preferably at least 1 °.

In a further embodiment according to the invention an average propagation direction of the incoming light wave is tilted with respect to each of the average propagation directions of the test waves. According to a further embodiment the tilt angle between the average propagation direction of the incoming light wave and the surface normal of the substrate is different from the tilt angle between the average propagation direction of the respective test wave and the surface normal. In this way measurement disturbances are reduced even further.

In a further embodiment according to the invention the diffractive structures are arranged regularly on the substrate. This way a large number of differently shaped optical surfaces can be measured efficiently by stepping the diffractive optical element between the subsequent measurements of different optical surfaces by a constant distance or rotating the same by a constant angle.

It is a further object of the invention to provide an object having an aspherical optical surface with an improved surface accuracy. This object is solved according to the invention by an object having an aspherical optical surface, which is symmetrical about a rotational axis traversing the optical surface at an apex of the optical surface, wherein a subarea of the optical surface is delimited by a circle around the apex having a radius of at least 5 mm and the RMSa-value of the surface subarea is at most 10% higher than the RMSa-value of the entire surface area of the optical surface.

The RMSa-value is defined in DIN ISO 101 10-5:2000-02. The manufacture of such an object is made possible by the above described measuring method according to the invention. Aspheres currently available have much larger RMSa- values in an on-axis region. The measuring method according to the invention allows a precise measurement of the deviations of the actual shape of the optical surface of the asphere from its target shape. Based on these measurements the optical surface can be properly machined in order to achieve the above-specified RMSa-values.

The above object is further solved by an object having an aspherical optical surface which is symmetrical about a rotational axis traversing the optical surface at an apex of the optical surface, wherein a subarea of the optical surface is delimited by a circle around the apex having a radius of at least 5 mm and the

RMSa-value of the surface subarea is at most 0.1 nm. Also the manufacture of this kind of asphere is made possible by the measuring method according to the invention. Due to inaccuracies in the measurement data of the on-axis area of such an asphere obtained by measuring methods currently available, the specified parameters currently cannot be met.

In an embodiment according to the invention the radius of the circle limiting the subarea is at least 10 mm. According to a further embodiment the aspherical optical surface has a maximum deviation from its best fitting sphere of more than 10 μm, preferably more than 100 μm, and more preferably more than 1 mm.

The features specified above with respect to the method according to the invention can be transferred correspondingly to the diffractive optical element according to the invention and vice versa. Advantageous embodiments of the diffractive optical element according to the invention and advantageous embodiments of the method according to the invention resulting therefrom shall be covered by the disclosure of the invention.

Brief description of the drawings

The foregoing, as well as other advantageous features of the invention, will be more apparent from the following detailed description of exemplary embodiments of the invention with reference to the following diagrammatic drawings, wherein:

Figure 1 illustrates an interferometric measuring apparatus for interferometrically measuring a deviation of an actual shape from a target shape of an optical surface of a test object according to a first embodiment of the invention;

Figure 2 illustrates a portion designated by Il of the interferometric measuring apparatus according to Figure 1 in more detail;

Figure 3 is a plan view of an optical surface tested by means of the interferometric measuring apparatus illustrated in Figures 1 and 2;

Figure 4 illustrates a portion of an interferometric measuring apparatus according to a second embodiment of the invention;

Figure 5 shows an exemplary line pattern of a diffractive optical element of any one of the interferometric measuring apparatuses illustrated in Figures 1 , 2 and 4;

Figure 6 illustrates a portion of an interferometric measuring apparatus according to a third embodiment of the invention;

Figure 7 illustrates several arrangement options for a spherical optical surface for measurement by means of the interferometric measuring apparatus according to Figure 6;

Figure 8 illustrates a portion of an interferometric measuring apparatus according to a fourth embodiment of the invention;

Figure 9 illustrates the effect of different tilt angles of a diffractive optical element according to the invention with respect to a test object;

Figure 10 illustrates a further embodiment of a diffractive optical element comprising several diffractive structures according to the invention;

Figure 11 illustrates the diffractive optical element according to Figure 10 in a first measuring position; and

Figure 12 illustrates the diffractive optical element according to Figure 10 in a second measuring position.

Detailed description of exemplary embodiments

In the embodiments of the invention described below, components that are alike in function and structure are designated, as far as possible, by the same or similar reference numerals. Therefore, in order to understand the features of the individual components of a specific embodiment, the descriptions of other embodiments or the summary of the invention should be referred to.

Figure 1 illustrates an interferometric measuring apparatus 10 according to a first embodiment of the invention. The interferometric measuring apparatus 10 is used for interferometrically measuring a deviation of an actual shape from a target shape of an aspherical optical surface 12 of a test object 14. The test object 14 can, for example, be a mirror or a transmissive optical lens, etc. The optical surface 12 has, in the shown embodiment, a rotationally symmetrical shape about a rotational axis 16 or asphere axis. The test object 14 is mounted on a test piece holder not shown in the drawing, which test piece holder is optionally rotatable around the rotational axis 16.

The interferometric measuring apparatus 10 comprises an interferometer 17, which interferometer 17 comprises a light source unit 18, a beam splitter 34 as well as an interferometer camera 68. The light source unit 18 comprises a laser 21 , such as a helium neon laser, emitting a laser beam 22 of coherent light at a wavelength of 632,8 nm. The laser beam 22 is focussed by a focussing lens 24 onto a pinhole aperture of a spatial filter 26 such that a diverging beam 28 of coherent light emerges from the pinhole. The wave front of the diverging beam 28 is substantially spherical. The diverging beam 28 is collimated by a group of lens elements 30 to form an illumination beam 19 having a substantially flat wave front. The illumination beam 19 travels along an optical axis 32 of the interferometer 17 and traverses the beam splitter 34.

The interferometer 17 illustrated in Figure 1 is of a Fizeau-type. It is to be noted, however, that the invention is not limited to such an interferometer. Any other type of interferometer, such as a Twyman-Green-type of interferometer, examples of which are illustrated in chapter 2.1 of the text book edited by Daniel Malacara, Optical Shop Testing, Second Edition, Wiley lnterscience Publication (1992), a Michaelson-type interferometer, examples of which are illustrated in chapter 2.1 of the text book edited by Daniel Malacara, a Mach-Zehnder-type of interferometer, examples of which are illustrated in chapter 2.6 of the text book edited by Daniel Malacara, a point-diffraction-type interferometer and any other suitable type of interferometer may be used.

The illumination beam 19 enters a Fizeau element 36 having a Fizeau surface 38. A portion of the light of the illumination beam 19 is reflected as a reference wave 40 by the Fizeau surface 38. The light of the illumination beam 20 traversing the Fizeau element 36 has a plane wave front 42 and is in the following designated as incoming light wave 20 with respect to a diffractive optical element 46 being arranged in its beam path. Optionally pre-shaping optics transforming the light of the illumination beam 19 having traversed the Fizeau element 36 can be arranged in the beam path for providing the incoming light wave 20 with a spherical wave front. In the example shown in Figure 1 , however, the incoming light wave 20 is a plane wave.

The diffractive optical element 46 comprises a hologram, which may be generated by exposing a photographic plate to reference light and light reflected from an optical surface having a surface corresponding to the target shape of the optical surface 12 at a high accuracy, or the hologram may be a computer generated hologram (CGH) generated by calculating a corresponding grating using a computer involving methods such as ray tracing and plotting the calculated grating on a surface of a substrate. The grating may, for example, be formed by a lithographic method.

The incoming light wave 20 is diffracted at a diffractive surface 48 of the diffractive optical element 46. The diffracted wave resulting therefrom is referred to as a test wave 44 which has a wave front in the shape of a target shape of the optical surface 12. The test wave 44 is therefore incident on the optical surface 12 in autocollimation. The test wave 44 is reflected at the optical surface 12. The wave front of the reflected test wave 44 contains the information on the deviation of the actual shape of the optical surface 12 from its target shape. In an alternative embodiment the test wave 44 traverses the optical surface 12 and is reflected by a subsequent mirror.

As further shown in Figure 1 the test wave 44 having interacted with the optical surface 12 travels back essentially in the beam path of the incoming light wave 20, traverses the Fizeau element 36, and a portion of the test wave 44 is reflected by the beam splitter 34. The test wave 44 reflected by the beam splitter 34 is imaged onto a photosensitive surface 62 of a camera chip 64 through an objective lens system 66 of the camera 68 such that the optical surface 12 is imaged onto the camera chip 64. A portion of the reference light 40 is also reflected by the beam splitter 34 onto the photosensitive surface 62 of the camera chip 64. The reference wave 40 and the test wave 44 generate an interference pattern on the photosensitive surface 62. The wave generated by superposition of the reference wave 40 and the test wave 44 is referred to as residual wave which generates the interference pattern. The interferometric measuring apparatus 10 further comprises evaluation means 70 which are adapted for determining the deviation distribution of the actual shape from the target shape of the optical surface 12 based on the measured interference pattern.

Figure 2 shows the portion of the interferometric measuring apparatus 10 according to Figure 1 designated by Il in more detail. Figure 2 shows the diffractive optical element 46 comprising a substrate 50 as well as the diffractive surface 48 which has a plane shape. The incoming light wave 20 is incident on the diffractive optical element 46 such that the propagation direction 52 of the incoming light wave 20 is tilted with respect to the surface normal 54 of the diffractive surface 48 by a tilt angle β. In an alternative embodiment, in which the wave front of the incoming light wave 20 is not plane, an average propagation direction of the incoming light wave 20 is tilted with respect to the surface normal 54 by the tilt angle β. As mentioned above, the test wave 44 generated by diffraction on the diffractive surface 48 from the incoming light wave 20 is incident on the optical surface 12 in autocollimation. Therefore, each single ray 56 and 56a, respectively, is perpendicular to the optical surface 12 at its respective location of incidence on the optical surface 12.

The optical surface 12 has, as mentioned above, an asphehcal target shape which is symmetrical about the rotational axis 16. The location of the optical surface 12 traversed by the rotational axis 16 is designated as apex 58 of the optical surface 12. The apex 58 is the center of a subarea 60 of the optical surface 12, which subarea 60 is delimited by a circle 72. The location of the subarea 60 within the optical surface 12 is shown in Figure 3 in a top view. The radius R of the circle 72 is at least 5 mm.

The rays of the test wave 44 being incident on the subarea 60 are designated by the reference numerals 56a. According to the embodiment of the diffractive optical element 46 shown in Figure 2 the single rays 56a are each tilted with respect to the surface normal 54 of the diffractive surface 48. Figure 2 illustrates three single rays 56a and their respective tilt angles γ-ι, γ ₂ and γ ₃ with respect to the surface normal 54. The single rays 56a deviate from the surface normal 54 by at least 0.1 °. The surface normal 54 of the diffractive surface 48 of the diffractive optical element 46 is tilted with respect to the rotational axis 16 by a tilt angle α.

The tilt angle α is at least 0.1 °. In the case shown in Figure 2 the rotational axis

16 coincides with the average propagation direction of the test wave 44 and the average surface normal of the optical surface 12. The tilt angle α is different from the tilt angle β. The propagation direction 52 of the incoming light wave 20 is tilted with respect to the rotational axis 16 by a tilt angle δ, which is the sum of the tilt angles α and β.

Figure 9 illustrates the effect of different tilt angles α. In the illustrated example the tilt angle β is constant at 10°. The single diagrams (a) - (f) show reflexes in a second diffractive order generated on the diffractive surface 48 from the light of the incoming light wave 20. The reflexes shown in the diagrams (a) - (f) are recorded at the photosensitive surface 62 of the camera chip 64. In diagram (a) of Figure 9 the tilt angle α is 0° resulting in a circular second order reflex. The following diagrams (b), (c), (d), (e) and (f) have been recorded for the tilt angles α of 0.4°, 0.8°, 0.9°, 1.2° and 1.8°, respectively. As can be seen from the diagrams

the second order reflexes are already reduced significantly at a tilt angle α of 0.4° and are further reduced at larger tilt angles α.

As mentioned above, none of the single rays 56a being incident on the subarea 60 of the optical surface 12 is perpendicular to the diffractive surface 48. In the embodiment shown in Figure 2 the off-axis rays 56 being incident on the optical surface 12 outside of the subarea 60 are not perpendicular to the diffractive surface 48 as well. According to the invention, however, off-axis rays can also be perpendicular to the diffractive surface. This is the case in an embodiment of the diffractive optical element 46 shown in Figure 4, in which a ray 56b of the test wave 44 is perpendicular to the diffractive surface 48 of the diffractive optical element 46. The position 74 of the ray 56b is located a distance D away from a center location 76 of the diffractive optical element 46 defined by the intersection of the rotational axis 16 with the diffractive surface 48. The distance D is large enough that the ray 56b is not incident onto the subarea 60 of the optical surface 12.

Figure 5 shows a diffractive structure 78 of the diffractive surface 48 of the diffractive optical element 46 of Figure 4. A Littrow-reflex is generated at the position 74 from the incoming light wave 20. This Littrow-reflex is not rotationally symmetric and can therefore be compensated for by conducting several measurements at different rotational positions of the test object 14 around the rotational axis 16 in a so-called "turn-averaging" method. As no Littrow-reflexes occur in an axial area, the optical surface 12 of the test object 14 according to Figures 2 and 4 can be manufactured such that the RMSa-value of the subarea 60 is at most 10% higher than the RMSa-value of the entire surface area of the optical surface 12. Further, the test object 14 can be manufactured, such that the RMSa-value of subarea 60 is at most 0.1 nm.

Figure 6 shows a third embodiment of a diffractive optical element 146 according to the invention. The diffractive optical element 146 differs from the diffractive optical element 46 according to Figures 2 and 4 in that the diffractive optical

element 146 is adapted for generating a test wave 44 having a spherical wave front. The diffractive optical element 146 is therefore adapted for measuring a test object 114 having a spherical optical surface 112. The diffractive optical element 146 is also configured for generating rays 56a being incident on a subarea 60 of the optical surface 112 being tilted with respect to the surface normal 56 on its diffractive surface 58.

The subarea 60 of the optical surface 112 is, as are the subareas 60 according to Figures 2 and 4, delimited by a circle around the apex 58 of the optical surface 112 having a radius R of at least 5 mm as projected onto the optical surface 112. The single rays 56a generated by the diffractive optical element 146 are also tilted with respect to the surface normal 54 of the diffractive surface 148 by at least 0.1 °. Figure 7 shows several optical surfaces 112a, 112b, 112c, 112d and 112e testable by means of the diffractive optical element 146. Each of the optical surfaces 112a, 112b, 112c, 112d and 112e has a different radius of curvature.

Figure 8 shows a fourth embodiment of a diffractive optical element 246 according to the invention. The diffractive optical element 246 differs from the diffractive optical elements 46 and 146 in that it is configured for generating a test wave 44 having a wave front in the shape of a so-called free form surface, that means the shape has no axis of symmetry. The diffractive optical element 246 is therefore adapted for testing a corresponding test object 214 having an optical surface 212 in the form of a free form surface.

Each single ray 56 of the test wave 44 is perpendicularly incident on the optical surface 212. Further, each single ray 56 is tilted with respect to the surface normal 54 of the diffractive surface 248 of the diffractive optical element 246. The tilt angles are indicated in Figure 8 for the rays 56 shown in the drawing by the tilt angles, γi to Vg wherein each of the angles γi to γ _g are at least 0.1 °. The tilt of the single rays 56 is achieved by tilting the surface normal 54 of the diffractive optical element 246 with respect to an average propagation direction 80 of the test wave

44 by the tilt angle α. Further, the tilt angle α is adjusted such that the diffractive surface 48 is at no point parallel to the optical surface 112.

Figure 10 shows a further embodiment of a diffractive optical element 346 according to the invention which comprises a single substrate 50 containing four circular diffractive structures 378a, 378b, 378c and 378d, each of which fulfils the function of one of the diffractive optical elements 46, 146 and 246 described above. The diffractive structures 378a, 378b, 378c and 378d are configured for diffracting the incoming light wave 20 and thereby generate separate test waves 44 being adapted to different target shapes.

The diffractive optical element 346 is mounted in an embodiment of the measuring apparatus 10, which is configured such that the diffractive optical element 346 can be moved to four different positions wherein in each of the positions a different one of the diffractive structures 378a, 378b, 378c and 378d is illuminated by the incoming light wave 20. Figures 11 and 12 illustrate two of these positions. In the position shown in Figure 11 the diffractive optical element 346 is arranged such that the incoming light wave 20 illuminates the second diffractive structure 378b. In the position illustrated in Figure 12 the diffractive optical element 346 is translated such that only the first diffractive structure 378a is illuminated by the incoming light wave 20. The test waves 44 generated by the respective diffractive structures 378a and 378b both have the same average propagation direction 80.

In a further embodiment of the interferometric measuring apparatus, the diffractive optical element 364 is rotatably mounted for switching the diffractive structures 378a, 378b, 378c and 378d to be illuminated by the incoming light wave 20. The embodiment of the diffractive optical element 346 illustrated in Figures 10 to 12 allows test objects with different optical surfaces to be tested cost efficiently with high accuracy.

List of reference numerals

10 interferometric measuring apparatus

12 optical surface

14 test object

16 rotational axis

17 interferometer

18 light source unit

19 illumination beam

20 incoming light wave

21 laser

22 laser beam

24 focusing lens

26 spatial filter

28 diverging beam

30 group of lens elements

32 optical axis

34 beam splitter

36 Fizeau element

38 Fizeau surface

40 reference wave

42 plane wave front

44 test wave

46 diffractive optical element

48 diffractive surface

50 substrate

52 propagation direction of incoming light wave

54 surface normal

56 single ray

56a single ray

56b single ray

58 apex

60 subarea

62 photosensitive surface

64 camera chip

66 objective lens system 68 camera

70 evaluation means

72 circle

74 position of perpendicular ray

76 center location 78 diffractive structure

80 average propagation direction

112 optical surface

114 test object

146 diffractive optical element 148 diffractive surface

212 optical surface

214 test object

246 diffractive optical element

248 diffractive surface 246 diffractive optical element

378a - 378d diffractive structures