Login| Sign Up| Help| Contact|

Patent Searching and Data


Title:
HOLOGRAPHIC IMAGING WITH BRIGHTNESS CONTROL
Document Type and Number:
WIPO Patent Application WO/2012/007763
Kind Code:
A1
Abstract:
A method of operating a laser in aa holographic imaging system. The method comprises calculating an intensity modulation level for the laser (100) to give a desired brightness of an image on a sceen (180) and embedding data representative of the desired brightness into data used for the information content of the image. The data representative of the desired brightness is extracted and applied to a driver of the laser whereas holographic data used for the information content of the image is addressed to a spatial light modulator (140).

Inventors:
CHRISTMAS JAMIESON (GB)
Application Number:
PCT/GB2011/051329
Publication Date:
January 19, 2012
Filing Date:
July 14, 2011
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
TWO TREES PHOTONICS LTD (GB)
CHRISTMAS JAMIESON (GB)
International Classes:
G03H1/22; G03H1/08; G03H1/32
Domestic Patent References:
WO2008099211A22008-08-21
WO2007131650A12007-11-22
WO2005059881A22005-06-30
Foreign References:
JP2008310067A2008-12-25
US20090109349A12009-04-30
Attorney, Agent or Firm:
KILBURN & STRODE LLP (London WC1R 4PJ, GB)
Download PDF:
Claims:
Claims

1. A method of operating a laser in an imaging system comprising:

calculating a modulation level for the laser to give a desired brightness of an image;

embedding data representative of the desired brightness into data used for the information content of the image;

extracting the data; and

applying it to a driver of the laser.

2. The method according to claim 1 further comprising writing data used for the information content of the image to a spatial light modulator.

3. The method according to any preceding claim wherein the image is a sub- frame in a temporal sequence of sub-frames.

4. The method according to claim 2 or 3 further comprising deriving the data representative of the desired brightness while the image information content is being written to the spatial light modulator.

5. The method according to claim 3 or 4 further comprising preparing the data for the next sub- frame including deriving the data representative of the desired brightness before the data is written to the spatial light modulator. 6. The method according to any preceding claim wherein the data representative of the desired brightness is contained within the least significant bit of the data used for the information content.

7. The method according to any preceding claim wherein the data used for the information content is holographic data representative of the image.

8. The method according to any preceding claim wherein the data representative of the desired brightness determines whether the laser is on or off for the sub -frame.

9. The method according to any preceding claim wherein the data used for the information content provides data for every phase-modulating element of the spatial light modulator and thereby enables formation of an image sub -frame, and at least one bit per modulating element is representative of brightness of the image sub-frame. 0. The method according to any preceding claim further comprising integrating the brightness data from the combined data for each phase-modulating element, and controlling the laser driver by the outcome of the integration.

11. An imaging system comprising:

a processor arranged to calculate a light modulation level to give a desired brightness of an image and provide data to an image display system, wherein the data comprises data representative of an image and data representative of the desired light modulation level;

a laser controller arranged to receive the data representative of the desired brightness of the image and modulator the brightness of a laser to provide the desired brightness of image.

12. An imaging system as claimed in claim 11 wherein the image display system is a spatial light modulator.

13. An imaging system as claimed in claim 11 or 12 wherein the data

representative of an image is holographic data representative of the image.

14. An imaging system as claimed in any of claims 11 to 13 wherein the data relates to a sub-frame of a 2D video sequence of image frames.

15. An imaging system as claimed in any of claims 11 to 14 wherein the data representative of the desired brightness is embedded in the least significant bit of the data.

Description:
HOLOGRAPHIC IMAGING WITH BRIGHTNESS CONTROL

The present invention relates to the field of image projection and image production. Embodiments use spatial light modulators in combination with laser light sources.

Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured on, for example, a photosensitive plate by well known interference techniques to form a hologram comprising interference fringes. The hologram may be reconstructed to form an image, or holographic reconstruction, representative of the original object by illuminating the hologram with suitable light.

Computer-generated holography may numerically simulate the interference process using Fourier techniques.

It has been proposed to use holographic techniques in a two-dimensional image projector.

In an example of a 2D image projection system, the data causes light modulating elements to vary in state, in some cases to change phase states. The spatial light modulator (SLM), for example liquid crystal on silicon (LCOS) SLM, forms an array of phase-modulating elements that has been derived in some way from an image to be displayed or is generated so as to display that image. Light representative of an object is transformable into a phase distribution in a number of ways, including algorithms such as Gerchberg-Saxton. The arm is to provide something related to a Fourier transform of the received light. Then the light modulating elements- sometimes referred to as "pixels" (although there is no correspondence between the state of a "pixel" and any specific location in the image or the object)- can form variable kino forms, for example where 2D representations are to be formed.

Referring to Figure 1, there is shown a light source 100 which applies light via a Fourier lens (120) onto a spatial light modulator (140) in this case as a generally planar wavefront. The spatial light modulator is reflective and consists of an array of a large number of phase-modulating elements. Light is reflected by the spatial light modulator and consists of two parts, a first specularly reflected portion (known as the zero order) and a second portion that has been modulated by the phase-modulating elements to form a wavefront of spatially varying phase. Due to the reflection by the spatial light modulator all of the light is reflected generally back towards the light source (100) where it impinges on a mirror with aperture (160) disposed at 45° to the axis of the system. All of the image part of the light is reflected by the mirror towards a screen (180) that is generally parallel to the axis of the system. Due to the action of the Fourier lens (120) the light that impinges on the screen (180) forms a real image that is a reconstruction of an image from which the information applied to the phase modulating elements was derived.

In applications such as real-time 2D video projection, for example, such spatial light modulators require data to be written to them very quickly.

In reconstructing the image into an image plane a light source is applied to the pixels. The resultant light, after phase (or other) modification by the pixels, may be passed via suitable optics, as required, to a screen. On the screen, a 2D reconstruction of the source image is formed.

In other examples of image production systems the image may be a virtual image. Image production systems using SLMs can also provide 3D imaging. When using more than one light source to create an image in cooperation with an SLM, for example in the case of colour imaging, there is a problem in that the light output of the light sources is likely to vary between sources. An example of the problem is for a system using a red a blue and a green laser with a single LCOS SLM that in combination with optics, for example including a Fourier lens, projects an image as a reconstruction of data applied to the SLM in an imaging plane.

Aspects of the invention are set out in the appended independent claims. In summary, the present disclosure relates to embedding data representative of the desired brightness into data used for the information content. Accordingly, there is provided an improved method for operating a laser in an imaging system. The inventor has recognised that in projection system operating in the Fourier domain the brightness of frames may vary widely since it is the frequency distribution that is illuminated during reconstruction.

This can be understood by considering, for example, a hologram computed to display an image of the night sky. When displayed using a phase only holographic projector (operating in the Fourier domain), this scene would appear to be substantially brighter than in the case when the same system displays a solid block of colour. This is because of the way phase only holography efficiently steers light to form an image. In particular, each pixel on the hologram contributes to multiple parts of the reconstructed image.

Given the potential for a wide variation in image brightness from one frame to the next in the Fourier domain, a fast and dynamic solution needs to be used to control the laser light sources to ensure that the brightness of the reconstructed image remains reasonable constant from frame to frame.

There is provided an improved system in which the laser on time is controlled in such a way that the system reduces the amount of noise generated by laser speckle.

Brief description of the drawings

Embodiments of the present invention will now be described to the accompanying drawings in which:

Figure 1 shows a schematic drawing of a SLM based projection system;

Figure 2 shows a schematic drawing of an example of a reflective SLM;

Figure 3 shows a schematic of a colour projector display;

Figure 4 shows a diagram of illumination time; Figure 5 shows a diagram of optimised illumination time;

Figure 6 shows a diagram of illumination control; and

Figure 7 shows a schematic drawing of a typical SLM device. In the figures like reference numerals referred to like parts.

Detailed description of the drawings

It is found that the phase information alone is sufficient to generate a hologram which can give rise to a holographic reconstruction of acceptable quality. That is, the amplitude information in the hologram can be discarded. This can reduce the power of the required laser light sources but has other advantages too. Fourier-based computer generated holographic techniques have therefore been developed using only the phase information.

The image reconstructed by a hologram is given by the Fourier transform of the hologram. The hologram is therefore a phase-only pattern representative of the Fourier transform of the object whereas the reconstructed image (or holographic reconstruction) may contain both amplitude and phase information.

Gerchberg-Saxton is one example of an iterative algorithm for calculating a phase only hologram from input image data comprising only amplitude information. The algorithm starts from a random phase pattern and couples this with amplitude data to form complex data. A discrete Fourier transform is performed on the complex data and the resultant dataset is the Fourier components, which are made up of magnitude and phase. The magnitude information is set to a uniform value, and the phase is quantised, to match the phase values available. An inverse discrete Fourier transform is then performed. The result is another complex dataset, where the magnitude information is overwritten by the target image and the process is repeated. The Gerchberg-Saxton algorithm therefore iteratively applies spatial and spectral constraints while repeatedly transferring a data set (amplitude and phase), between the spatial domain and the Fourier (spectral) domain. The Gerchberg-Saxton algorithm and derivatives thereof are often much faster than other "non-Fourier transform" algorithms such as direct binary search algorithms. Modified algorithms based on Gerchberg-Saxton have been developed - see, for example, published PCT application WO 2007/131650 incorporated herein by reference.

These improved techniques are able to calculate holograms at a sufficient speed that 2D video projection is realised. Embodiments described herein relate to 2D video projection using a computer-generated hologram calculated using such a modified Gerchberg-Saxton algorithm

Holo graphically generated 2D video images are known to possess significant advantages over their conventionally projected counterparts, especially in terms of definition and efficiency. However, the computational and hardware complexity of the current hologram generation algorithms preclude their use in real-time applications. Recently these problems have been solved - see, for example, published PCT application WO 2005/059881, incorporated herein by reference. To display the phase only holographic data, a phase modulating device is required.

Since these devices do not modulate the amplitude, they are optically transparent, in general. Therefore no light is lost to absorption, for example. This has the major advantage that all of the reconstruction light is used in the creation of the holographic reconstruction. This translates to a more energy efficient display system.

The phase modulating device may be pixellated and each pixel will act as a diffractive element. The diffraction pattern from each pixel will cause a complex interference pattern at a screen referred to as a replay field. Due to this complex relationship, each pixel on the hologram contributes to multiple parts of the reconstructed image.

An example phase modulating device is a spatial light modulator (SLM). Typically a SLM has a field of addressable phase-modulating elements. In some SLMs the phase- modulating elements are a linear or one-dimensional array of elements; in others a two dimensional array are provided. For simplicity many SLMs have a regular 2-D array of like, generally square, phase-modulating elements; it is however not necessary for the phase-modulating elements to be alike in size or shape.

Figure 2 shows an example of using a reflective SLM, such as a LCOS SLM, to produce a holographic reconstruction at a replay field location, in accordance with the present disclosure.

A light source (210), for example a laser or laser diode, is disposed to illuminate the LCOS SLM (240) via a collimating lens (211). The collimating lens causes a generally planar wavefront of light to become incident on the SLM. The direction of the wavefront may be slightly off-normal (i.e. two or three degrees away from being truly orthogonal to the plane of the transparent layer. The arrangement is such that light from the light source is reflected by a reflective rear surface of the SLM and by interaction with a phase modulating layer to form an exiting wavefront (212). The exiting wavefront is applied to optics including a Fourier transform lens (220), having its focus at a screen (225).

The Fourier transform lens receives light from the SLM and performs a frequency- space transformation to produce a holographic reconstruction at the screen (225) in the spatial domain.

In this process, the light from the light source is generally evenly distributed across the SLM (240), and across the phase modulating layer. Light exiting the phase- modulating layer may be distributed across the screen. There is certainly no correspondence between a specific image region of the screen and any one pixel of the SLM.

Figure 3 shows an exploded diagram of a projector assembly having a red (302), a green (304) and a blue laser (306) with optical systems directing light to a LCOS

SLM (307). The SLM in this case is a phase-only SLM. The SLM has a driver (308) to supply electrical signals to it, and these signals cause the elements of the LCOS (307) to display a hologram that is to be reconstructed on a screen. The electrical signals thus constitute, or are related to, the information content of the image. The light from the LCOS (307) is passed to a Fourier lens (310) to allow reconstruction of the phase data distribution of the LCOS (307) onto a screen.

Figure 3 further shows the assembly comprising a video interface (312), a plurality of beam steering mirrors (314), a mirror comprising a zero order block (316), a Fourier lens holder (318), a LCOS guide (320) and a LCOS mount and flexible substrate (322) One approach in driving the lasers is a simple frame-sequential colour sequence (FSS) which allocates time within one video frame. In one example, each colour slot is equally weighted in time.

However this does not necessarily have to be the case. If one of the laser light sources is significantly brighter than the others, then in one set-up the laser power of the bright laser is modulated down, keeping its time slot identical to the others. In another the higher power is permitted and the time slots rebalanced accordingly.

In the case of an example of a projector, the light sources used were as in table 1:-

Table 1

Given the large amount of blue power, the distribution of time slots was set such that more time was given to red and green lasers than to the blue. To accurately determine the duration of time slots consideration needs to be given to the balance of power needed to create an image with an acceptable colour temperature. A typical projector has a colour temperature of 8200 which has x w = 0.293, y w = 0.303 on the CIE 1931 colour space chromaticity diagram

Using Equation 1 with a 10 lumen specification , the tristimulus Χ,Υ,Ζ values are derived .

10

Y - x

= 9.67 Y · (1 - x w - )

13,33

yw

Equation 1

Given the chosen laser light sources, the colour co-ordinates were looked up in the CIE Colour matching function charts, from which measurements as shown in Table 2 were derived:-.

Table 2

The power level for each laser is given by Equation 2

Equation 2

The quoted powers above assume a 100% efficient projector which cannot be the case; optimal efficiency can be derived by considering the different losses in the system.-see Table 3

Table 3

Given the predicted losses, the laser power required is shown in Table 4 Red Green Blue

Laser Pow r 29.8mW 25.12mW

Las*r power scaled

T34.9mW 90.3mW 76.4mW

for 3¾¾ duty cycle.

Table 4 Having established the power requirements of the laser, it can be concluded that the lasers are over specified. This however can be advantageous, if the lasers are operated at 90% of their maximum power, their illumination time can be

reconsidered, as shown in Table 5 and Figure 4.

Table 5

Figure 4 shows the red light pulse (402), the green light pulse (404) and the blue light pulse (406).

This illumination pattern works well in a holographic system, given that the liquid crystal has a finite rise and fall time, the greatest change that could take place from one sub frame to the next would be a swing from 2π to zero and due to the slow fall time this should define the minimum settling time (3.39mS @ 45C). As the blue laser is on for a very short period of time, a proportion of the unused illumination time could be used to improve the liquid crystal stability during the red illumination time as shown in Figure 5. Figure 5 shows the temporally shifted red light pulse (502), green light pulse (504) and blue light pulse (506).

This illumination level assumes a white screen; however as the image content changes there is a need to reduce the lasers' power from their current levels in line with the total power requirements of the scene.

This is achieved by the fact that the hologram contains the laser modulation information.

In one embodiment, this is possible because the system of the embodiment only has 16 phase levels i.e. 4 bits. This means that the upper 4 bits of an 8 bit data bus are utilised for the phase modulation with the lower bits available to carry laser modulation information.

In an alternative embodiment, the least significant bit of the phase modulation data is used to control the laser illumination, this data is altered in such a way that the image quality is not impacted and yet the correct amount of laser power is generated. In response to the bit being set, the laser is driven at 90% of its maximum capacity, and when the bit unset the laser is disabled.

In a set-up where a specified bit (eg bit 1) of each pixel forms the laser control data, that bit per pixel from the stream of hologram data bytes can be fed to a laser controller. For the population of pixels of data forming a subframe there will be a number of bits set and a number of bits unset. If all are set, the laser will be operated at maximum brightness (90% in this example) if none is set then at minimum brightness. The number of bits is effectively integrated across the subframe period.

Advantageously, because each laser is effectively switched on and off rapidly to provide optical modulation, the system is self-despeckling. That is, the noise created by laser speckle is reduced. The despeckling effect occurs due to the heating and cooling of the temporally modulated laser, this is turn alters the lasing wavelength of a laser diode, however this in itself is not sufficient to despeckle the image. It is understood that the phase modulation created by an SLM alters with time, known as phase ripple. This phase ripple effect can also be used to assist with the laser despeckling by utilising the micro variations is phase that occur. By flashing the laser on and off as proposed previously, the light will illuminate the phase distribution which is altering in time. This makes each flash of laser light reconstruct a substantially similar image which has a unique phase distribution and therefore a unique speckle pattern. The eye then integrates these unique speckle patterns and the apparent contrast speckle is reduced as shown in Equation 3, where N is the number of statistically independent speckle patterns.

Equation 3

In embodiments, the amount of time each laser is on for is determined by monitoring the magnitude of the Fourier transform signal in the computational algorithm. For example, if the Fourier transform signal for one colour is considered to be too high, more of the specified data bits carrying the brightness information will be set to off so as to reduce the overall laser on time and therefore the brightness of that colour. The data bit may be grouped or distributed in time.

It is alternatively possible to take other measures, for example summing the number of bits in a separate process. In this case the summed result is used to control the modulation of the relevant laser.

The on time may be determined as shown in Equation 4. Tv

x - y

Equation 4

Where:

Tv is video frame time

X is the number of pixels in the x-axis (1280)

y is the number of pixels in the y-axis (768)

Lt is the laser on-time; and

Pen is the pixel representation of the laser on time.

From Equation 4 we can determine the number of pixels required to control the laser with the results shown in Table 6 and Figure 6. Figure 6 shows the red illumination time 602, the green illumination time 604 and the blue illumination time 606.

Table 6

Although semiconductor lasers are able to respond to adjacent pixels being set and cleared, some types of laser are not able to achieve the necessary response time. For example if as a green laser, a solid state frequency doubled laser is used, this cannot achieve this response time, with a minimum response time of 25 μβ, this is the equivalent of 1474 pixels, or just over one video line. In experiments this reduced the bit depth of the green from 17 to 8bits. It should be made clear that the bit depth is in addition to the grey level control exerted through the floating point hologram calculations.

The invention is not restricted to phase-only SLMs, nor to 2D systems. In embodiments, the spatial light modulator is a Liquid Crystal over silicon (LCOS) device. The image quality is, of course, affected by the number of pixels and the number of possible phase levels per pixel.

LCOS devices are a hybrid of traditional transmissive liquid crystal display devices, where the front substrate is glass coated with Indium Tin Oxide to act as a common electrical conductor. The lower substrate is created using a silicon semiconductor process with an additional final aluminium evaporative process being used to create a mirrored surface, these mirrors then act as the pixel counter electrode. Compared with conventional glass substrates these devices have the advantage that the signal lines, gate lines and transistors are below the mirrored surface, which results in much higher fill factors (typically greater than 90%) and higher resolutions.

LCOS devices are now available with pixels between 4.5 μηι and 12 μηι, this size is determined by the mode of operation and therefore amount of circuitry that is required at each pixel.

The structure of an LCOS device is shown in Figure 7. A LCOS device is formed using a single crystal silicon substrate (702). It has a 2D array of square planar aluminium electrodes (701), spaced apart by a gap (701a), arranged on the upper surface of the substrate. Each of the electrodes (701) can be addressed via circuitry (702a) buried in the substrate (702). Each of the electrodes forms a respective planar mirror. An alignment layer (703) is disposed on the array of electrodes, and a liquid crystal layer (704) is disposed on the alignment layer (703). A second alignment layer (705) is disposed on the liquid crystal layer (704) and a planar transparent layer (706), e.g. of glass, is disposed on the second alignment layer (705). A single transparent electrode (707) e.g. of ITO is disposed between the transparent layer (706) and the second alignment layer (705).

Each of the square electrodes (701) defines, together with the overlying region of the transparent electrode (707) and the intervening liquid crystal material, a controllable phase-modulating element (708), often referred to as a pixel. The effective pixel area, or fill factor, is the percentage of the total pixel which is optically active, taking into account the space between pixels (701a). By control of the voltage applied to each electrode (701) with respect to the transparent electrode (707), the properties of the liquid crystal material of the respective phase modulating element may be varied, thereby to provide a variable delay to the portion of the wavefront of light from the collimating lens (711) that is incident thereon. The effect is to provide phase-only modulation to the wavefront, i.e. no amplitude effect occurs. A major advantage of using a reflective LCOS spatial light modulator is that the liquid crystal layer is half the thickness that it would be if a transmissive device were used. This greatly improves the switching speed of the liquid crystal (a key point for projection of moving video images). A LCOS device is also uniquely capable of displaying large arrays of phase only elements in a small aperture. Small elements (typically approximately 10 microns) result in a practical diffraction angle (a few degrees) so that the optical system does not require a very long optical path.

It is easier to adequately illuminate the small aperture (a few square centimetres) of a LCOS SLM than it would be for the aperture of a larger liquid crystal device. LCOS SLMs also have a large aperture ratio, there is very little dead space between the pixels (as the circuitry to drive them is buried under the mirrors). This is an important issue to lowering the optical noise in the replay field. The above device typically operates within a temperature range of 10°C to around 50°C, with the optimum device operating temperature being around 40°C to 50°C.

As a LCOS device has the control electronics embedded in the silicon backplane, the Fill factor of the pixels is higher, leading to less unscattered light leaving the device.

Using a silicon backplane has the advantage that the pixels are optically flat, which is important for a phase modulating device.

By using a sufficiently fast spatial light modulator, an appropriate computational algorithm and by writing data appropriately to the spatial Hght modulator it is possible to image different sub-frames of data at different apparent depths. The SLM must be sufficiently fast to allow information to be electrically written and optically read-out multiple times in a standard video frame.

The quality of the reconstructed hologram is also affect by the so-called zero order which is a consequence of the diffractive nature of the reconstruction.

Such zero-order light can be regarded as "noise" and includes for example specularly reflected light, and other light that is unrefr acted by the patterns on the spatial light modulator.

This "noise" is generally focussed at the focal point of the Fourier lens, leading to a bright spot at the centre of a reconstructed hologram.

Conventionally, the zero order light is simply blocked out however this would clearly mean replacing the bright spot with a dark spot.

However as the hologram contains three dimensional information, it is possible to displace the reconstruction into a different plane in space see, for example, published PCT application WO 2007/131649 - incorporated herein by reference. An alternative method to producing a colour holographic reconstruction, is referred to as "spatially separated colours" (SSC) involves all three lasers being fired at the same time, but taking different optical paths, e.g. each using a different SLM, and then combining to form the colour image.

An advantage of the frame-sequential colour (FSC) method is that the whole SLM is used for each colour. This means that the quality of the three colour images produced will not be compromised because all pixels on the SLM are used for each of the colour images. However, a disadvantage of the FSC method is that the overall image produced will not be as bright as a corresponding image produced by the SSC method by a factor of about 3, because each laser is only used for a third of the time. This drawback could potentially be addressed by overdriving the lasers, or by using more powerful lasers, but this would require more power to be used, would involve higher costs and would make the system less compact.

An advantage of the SSC (spatially separated colours) method is that the image is brighter due to all three lasers being fired at the same time. However, if due to space limitations it is required to use only one SLM, the surface area of the SLM can be divided into three equal parts, acting in effect as three separate SLMs. The drawback of this is that the quality of each single-colour image is decreased, due to the decrease of SLM surface area available for each monochromatic image. The quality of the polychromatic image is therefore decreased accordingly. The decrease of SLM surface area available means that fewer pixels on the SLM can be used, thus reducing the quality of the image. The quality of the image is reduced because its resolution is reduced.

The present disclosure is equally applicable to at least FSC and SSC.

Some embodiments implement the technique of "tiling", in which the surface area of the SLM is further divided up into a number of tiles, each of which is set in a phase distribution similar or identical to that of the original tile. Each tile is therefore of a smaller surface area than if the whole allocated area of the SLM were used as one large phase pattern. The smaller the number of frequency component in the tile, the further apart the reconstructed pixels are separated when the image is produced. The image is created within the zeroth diffraction order, and it is preferred that the first and subsequent orders are displaced far enough so as not to overlap with the image and may be blocked by way of a spatial filter.

As mentioned above, the image produced by this method (whether with tiling or without) comprises spots that form image pixels. The higher the number of tiles used, the smaller these spots become. If one takes the example of a Fourier transform of an infinite sine wave, a single frequency is produced. This is the optimum output. In practice, if just one tile is used, this corresponds to an input of a single phase of a sine wave, with a zero values extending in the positive and negative directions from the end nodes of the sine wave to infinity. Instead of a single frequency being produced from its Fourier transform, the principle frequency component is produced with a series of adjacent frequency components on either side of it. The use of tiling reduces the magnitude of these adjacent frequency components and as a direct result of this, less interference (constructive or destructive) occurs between adjacent image pixels, thereby improving the image quality. Preferably, each tile is a whole tile, although it is possible to use fractions of a tile.

The invention is not restricted to the described embodiments but extends to the full scope of the appended claims.