GB2350961A

GB2350961A - Determining optical aberrations and compensating therefor in computer generated holograms

Info

Publication number: GB2350961A
Application number: GB9913265A
Authority: GB
Inventors: Douglas A Pain; Christopher William Slinger
Original assignee: UK Secretary of State for Defence
Current assignee: UK Secretary of State for Defence
Priority date: 1999-06-09
Filing date: 1999-06-09
Publication date: 2000-12-13
Also published as: WO2000075733A1; CA2375514A1; AU4598900A; JP2003501697A; GB9913265D0; TW516005B; EP1183572A1

Abstract

A method is recited for generating data for application to a spatial light modulator 6 of a holographic display to display a three dimensional holographic image 8. The method comprises determining the aberration of light at optical components 12 of the holographic display, and defining said data to compensate for the effects of the determined aberration.

Description

2350961 Aberration Control of Images from Computer Generated Holograms The

present invention relates to computer generated holographic images.

Holography is a technique for generating 3D images having all the depth cues present. Computer generated holograms (CGH) are an important method for creating images of non-existent (or synthetic) objects. Provided the synthetic image can be described by some form of data structure, a computer can then calculate the holographic pattern in some design plane. This is equivalent to the interference pattern recorded by a photosensitive material in conventional (interferometric) hologram formation. The calculated CGH pattern is then applied to a spatial light modulator (SLM) which modulates readout light incident upon it. This modulated light propagates to yield the desired 3D image which can be viewed by a human observer.

A concern with holographic displays is maximising both image size I and the associated field of view FOV. As one might expect from the brightness theorem, for a given CGH, increasing I generally results in a corresponding decrease in FOV. To a good approximation

I. FOVAz constant Techniques which can increase the value of this product are important, as invariably it is the I and/or FO V constraints which determine the complexity of the CGH process, rather than image resolution concerns.

The inherent resolution limitations of the CGH SLM displays necessitate that the light diffracted by the CGH is magnified by scaling optics to generate images of the required size Iand field of view FOV(the FOVis a quantity defining the region in which an observer's eyes have to be positioned to see all of the image generated by the hologram). If a conventional approach is taken, these optics invariably introduce distortions and aberrations in to the scaled images. For high-end applications, such degradations in image quality may be unacceptable.

2 Previous attempts to correct for aberrations introduced by scaling optics have included the concept of a phase screen multiplier, as described for example in Maeno K, Fukaya N, Nishikawa 0, Sato K, Honda T, "Electro- holographic display using 15Mega pixels LCD", Proc SPIE, vol. 2652, p.15- 23 (1996). The phase screen multiplier involves the multiplication of a hologram by a two dimensional phase distribution which is independent of the image being reconstructed. Unfortunately, this technique relies on a paraxial approximation, so large images of significant FOV can only be corrected with limited success.

According to the present invention there is provided a method of generating computer generated hologram (CGH) data for application to a spatial light modulator of a holographic display to display a three dimensional holographic image, the method comprising: determining the aberration of light at optical components of the holographic display; and defining said CGH data to compensate for the effects of the determined aberration.

Thus a CGH can be designed to fully or partially compensate for the effects of the optical components. The pattern applied to the SLM can be generated so that a perfect or nearly perfect holographic image is formed by the display.

The determination of the aberration caused by the optical components may be perforined by a number of techniques, but preferably comprises determining the path length of light rays introduced by the optical components.

The path length of light rays between the spatial light modulator and the three dimensional holographic image may therefore be used in the definition of said CGH data.

The CGH data may be defined so that light emitted from the spatial light modulator compensates for the aberrations introduced by the optical components.

3 In order to minimise computer memory requirements without introducing excessive computing time overheads, an interpolation function may preferably be used to determine the path length of the light rays between the spatial light modulator and the three dimensional holographic image.

Alternatively or as well, the results of the determination of the aberration of light introduced by the optical components of the display may be saved in a look-up table. This is particularly useful for applications where reconfigurable or dynamic images are required to be generated.

The optical system may be designed to exhibit particular aberrations such that, when aberration compensation is carried out in the definition of the CGH data, increased field of view in the three dimensional holographic image is achieved.

The optical components may comprise one or more curved mirrors. In such a case, the compensation for the effects of aberration may be effected by determining the position and orientation of an image generated by the spatial light modulator on the basis of the viewing angle of an observer, so as to generate a three dimensional holographic image behind the convex mirror which appears stationary as the observer moves.

According to a second aspect of the invention, there is provided a holographic display comprising: a computer arranged to generate and / or store computer generated hologram (CGH) data; a spatial light modulator coupled to the computer for receiving the CGH data; optical components arranged in the light path of the spatial light modulator for causing a three dimensional holographic image to be displayed; wherein the CGH data is defined to compensate for the effects of the aberration of light caused by said optical components.

4 According to a third aspect of the invention, there is provided a computer storage medium having stored thereon computer generated hologram (CGH) data intended to form a light modulation pattern at a spatial light modulator of a holographic display, said CGH data including compensation for the effects of aberrations occurring at optical components of the display.

It will be appreciated that the use of the term "aberration" is intended to refer to distortions, rotations, translations etc. which would otherwise cause the displayed image to deviate from the intended holographic image. Aberrations may result from the use of either perfect or non-perfect optical components.

For a better understanding of the present invention and in order to show how the same may be carried into effect reference will now be made, by way of example, to the accompanying drawings, in which:

Figure I illustrates the coherent raytrace method for generating a computer generated hologram; Figure 2A illustrates imperfect monochromatic imaging of 3 collinear points in an offaxis parabolic mirror system; Figure 2B illustrates the imperfect imaging of the three points of Figure 2A in more detail; Figure 3 shows a corrected CGH producing 4 collinear diffraction limited points; Figure 4 illustrates the calculation of the optical path from points on the image to respective CGH sample points; Figure 5 shows three different views of an image; and Figure 6 shows an increase in viewing angle obtainable with a curved mirror.

The fundamental task of holographic generation is to generate a pattern which will diffract light to produce a required 3D image. Conventionally, in order to achieve this, first an object is illuminated with coherent light. The light from the object propagates to a design plane. From a knowledge of the light field at the design plane, it is possible to generate a reversed light field which, when created, will allow reproduction of the required 3D image in space. Holography is the technique which makes this process possible, as it stores and allows replay of the complex light field pattem in the design plane.

Computer generated holography (CGH) allows this process to be done for synthetic (non-existent) objects. The first stage in determining the required CGH pattem is to calculate the electric field distribution which would be generated by the synthetic object. The required pattern to be applied to a spatial light modulator (SLM) is determined from this electric field distribution at the design plane.

Figure I shows a technique used to determine the pattern applied to a SLM at the design plane for a typical CGH. A data field is generated for the coordinates in space of an imaginary object 2, relative to a design plane 4. The design plane is pixellated, and light rays are traced coherently to each pixel from each point on the object 'visible' from that pixel. The complex electric fields caused by each light ray are coherently summed at each pixel. Sophisticated radiosity models can be incorporated to determine accurately the strength of light rays (specular and diffuse reflection from the object surfaces, multiple light sources and reflections). Occlusion effects are automatically included, as only light rays from the part of the object 'visible' at a particular pixel are 'traced' and contribute to that pixel's electric field strength. This technique is known as Coherent Raytrace Technique (CRT)

Having calculated the complex electric field at the design plane, this information must be stored in some modulating structure, prior to being replayed by a light wave to generate the required 3D image. The technique of holography, with its concept of a reference wave, allows complex electric field distributions to be stored as real

6 quantities. This permits the use of amplitude or phase modulated systems to generate the required 3D images.

In order to generate an image of the required size, scaling optics are normally provided. Figure 2A shows a simple ray trace analysis of a CCH 6 designed in the usual way to generate three collinear points 8, equidistant from the eyes of an observer 10, using an off-axis parabolic mirror 12. The raytrace analysis, shown in more detail in Figure 2B, shows that blurred points are generally reconstructed. Although the central point 14 is sharp and in the desired position, the two points 16, 18 on either side are both blurred and no longer in the plane required - the light rays 20 do not all cross at the required points in space, or indeed at any single location. The images 16, 18 of these outer points would therefore appear to an observer to be in incorrect positions and blurred, and their apparent positions would shift with the location of the observer.

These effects can be corrected, provided the CGH is appropriately designed. The correction technique can be regarded as a backward raytrace. For the system shown, the paths of rays 20 from each of the object points 14, 16, 18 to the sample points on the CGH design plane 6 are calculated. The path length information determines the corrected CGH pattern at the design plane 6, such that, if the CGH is constructed and replayed, the images of the three points will be properly generated as diffraction limited points in the correct (i.e. design) locations. The correction in the CGH pattern at the design plane 6 due to the different path lengths is performed when the coherent summing of complex electric fields takes place as described above. In other words, the behaviour of the light through the optics after it has left the SLM is used when calculating the CGH pattern applied to the SLM.

Figure 3 shows such a system in operation. In the example shown there are four collinear object points 22, 24, 26, 28 and they have all been defined accurately in the same plane, i.e. without blurring or drifting.

Although the above is a simple example, the technique is, in principle, applicable to the generation of near arbitrary 31) images through a variety of imperfect optical elements, provided the characteristics of the optical elements are known a priori.

7 The ability to compensate for a wide range of optical elements is important. For example, the use of spherical optical forms (as opposed to aspherics used in the figures above) can allow cost savings, these being particularly significant for the large aperture optics sometimes required for systems containing high complexity CGH.

An important consideration is the computational requirements in the above approach. Determination of the required optical paths, for images having significant volume through multielement systems, is non-trivial. Even for the single element system shown in Figure 2, no general analytic solutions for the optical paths can be determined - typically numerical solutions using Fermat's principle have to be used.

For applications where reconfigurable or dynamic images are required to be generated, it is likely that a look-up table approach (based on precalculated information for the optical system in question) may be necessary, rather than real time calculation of optical path length. A further simplification is also possible by noting that the path lengths typically vary slowly through the object space and the CGH design plane. It is therefore fairly accurate to calculate the optical path length values at a few evenly spaced "sample" points, then fit a curve based on these values to allow interpolation for points other than sample values. It is therefore possible to use a simple interpolation function to minimise computer memory requirements without introducing excessive computing time overheads.

Figure 4 shows a representation of the optical path calculation from a point 30 on an image with co-ordinates {x,,,yp,z,,}, to the CGH sample point 32 with co-ordinates {x,,y,zJ for a specific optical element shape 0. This requires a numerical solution. In the Figure, a mirror surface is assumed and the ray path calculation requires determination of the position 34 at which the ray strikes the mirror, with co-ordinates {Xne,YM,Zm) - A CGH can be thought of as providing different images according to the observer's angle of view. Typically these images would be the appropriate perspective views as expected for a real object, but this need not be the case. For the case of an observer viewing the image of a cube produced by a CGH, the limited range of viewing angles inherent in the CGH replay means that the observer would normally only be able to see a small way round the sides of the cube. By designing the CGH such that its replay appears to rotate as the viewing angle moves off axis, the observer can 'see' further round the sides.

Figure 5 demonstrates this technique, and shows how, by rotating the image as the viewing angle changes, an observer can see further round the image of a cube. In Figure 5A an observer 36 views the image of a cube 40 from nearly straight onto one of its faces, i.e. substantially along the axis 38. In Figure 5B the observer 36 has increased the viewing angle by moving away from the axis 38, and the image of the cube 40 has rotated in the opposite direction, allowing him to see more of the top face. In Figure SC the observer 36 has moved even further, and the image of the cube 40 has rotated so far that he is almost looking directly at the top face. This means, of course, that the image no longer behaves like a real object (which may be undesirable) and it is necessary to identify an aberrating or non-imaging optic that makes the image appear stationary whilst still permitting a wide viewing angle.

Initial considerations with simple optics indicate that the concept is not unreasonable. Inspired by 'hall of mirrors' effects, an illustration of this can be made, as shown in Figure 6. One can envisage the points in a CG11 image as only 'emitting' light into a relatively small cone of angles (which results in that point being visible from only a small range of angles). If these rays impinge on a convex curved mirror one can see that on reflection, they are splayed out, effectively increasing the viewing angle. Now when viewing objects in such curved mirrors the image appears to rotate, following the observer's viewing angle. It is possible to effectively cancel this rotation in the CGH design. However, it is also apparent that the object appears to move with viewing angle. This can be compensated for as well, although the limited image volume available for the CGH replay will restrict the range of positions that can be used, and hence the size of the image.

9 When an observer 42 views the system along the axis 48 of a convex mirror 44, an image 46 generated by the CGH (not shown) is located on the axis 48, so that the reflection 50 (and thus the image seen by the observer) is located on the axis behind the mirror 44. When the observer 52 moves off axis and therefore looks from a different angle, the phase information in the CGH can be arranged so that the image 46 generated by the CGH has moved and rotated to a new position 54. In other words the data encoded at the SLM uses information about the behaviour of the light after it has left the SLM to provide a different image when the observer looks at a different part of the CGH. When the off-axis observer 52 views the system, the reflection 50 of the image 54 will appear to be in the same position as when the system was viewed along the axis. However, the diffraction angle relative to the axis of the image is still small. A beam splitter (not shown) is required to allow viewing of the reflected image without it being obscured by the CGH display system.

It will be appreciated by those skilled in the art that the invention is not limited by the embodiments described above. For example, the technique has been described for CGHs calculated by the coherent raytrace technique (CRT), whereas the invention will work for a CGH calculated by any technique. A coherent raytrace could be used to determine the aberration correction required even if the eventual CGH is not designed by the CRT method. The aberration compensation could also be achieved by examination of test images produced by the CGH in an actual system, altering the CGH iteratively until the required image is produced.

Claims

CLAIMS:

1. A method of generating computer generated hologram (CGH) data for application to a spatial light modulator of a holographic display to display a three dimensional holographic image, the method comprising: determining the aberration of light at optical components of the holographic display; and defining said CGH data to compensate for the effects of the determined aberration.

2. A method as claimed in claim 1, wherein the determination of the aberration of light at the optical components comprises determining the path length of light rays introduced by the optical components.

3. A method as claimed in claim 1 or 2, wherein the path length of light rays between the spatial light modulator and the three dimensional holographic image is used in the definition of said CGH data.

4. A method as claimed in claim 1, 2 or 3, wherein the data is defined so that light emitted from the spatial light modulator compensates for the aberrations introduced by the optical components.

5. A method as claimed in any preceding claim, wherein an interpolation function is used to determine the path length of the light rays between the spatial light modulator and the three dimensional holographic image.

6. A method as claimed in any preceding claim, wherein the results of the determination of the aberration of light introduced by optical components of the display are saved in a look-up table.

7. A method as claimed in any preceding claim, wherein the optical system is designed to exhibit particular aberrations such that, when aberration compensation is carried out in the definition of the CGH data, increased field of view in the three dimensional holographic image is achieved.

8. A method as claimed in any preceding claim, wherein the optical components comprise one or more curved mirrors.

9. A holographic display comprising: a computer arranged to generate and / or store computer generated hologram (CGH) data; a spatial light modulator coupled to the computer for receiving the CGH data; optical components arranged in the light path of the spatial light modulator for causing a three dimensional holographic image to be displayed; wherein the CGH data is defined to compensate for the effects of the aberration of light caused by said optical components.

10. A computer storage medium having stored thereon computer generated hologram (CGH) data intended to form a light modulation pattern at a spatial light modulator of a holographic display, said CGH data including compensation for the effects of aberrations occurring at optical components of the display.

11. A method of generating data for application to a spatial light modulator of a holographic display to display a three dimensional holographic image substantially as hereinbefore described with reference to the accompanying drawings.

12. A holographic display substantially as hereinbefore described with reference to the accompanying drawings.

13. A computer storage medium substantially as hereinbefore described with reference to the accompanying drawings.