GB2482864A

GB2482864A - Holographic waveguide display with distortion compensation

Info

Publication number: GB2482864A
Application number: GB1013656.2A
Authority: GB
Inventors: Shunyi Tan
Original assignee: Individual
Current assignee: Individual
Priority date: 2010-08-16
Filing date: 2010-08-16
Publication date: 2012-02-22
Also published as: GB201013656D0

Abstract

A display system employs an algorithm for generating holograms for a wedged waveguide panel, the wedged waveguide fit for that algorithm and apparatus for projecting holograms in the wedge waveguide. The display system includes a holographic projection system 12 and wedge shape waveguide panel 11. The holographic projection system projects holograms, kinoforms with special calculation, into the waveguide. After propagation, they will be replayed as the target images on the screen. The algorithm, named inverse wedge transform and employing a Fourier transform, is use to calculate and compensate the distortion caused by light injecting into the wedge interface. A wedge transform algorithm is used to calculate how waves propagate in the waveguide.

Description

BACKGROUND OF THE INVENTION

Field of the Invention

This invention is concerned with an algorithm for calculating holograms in a waveguide display and the design for a kind of waveguide, for which that algorithm can be applied.

General Background of the invention

Tapered-waveguide display comprising a video projector, a flat slab waveguide, and a tapered waveguide is described in WO 01/72037. Comparing with normal flat-panel displays such as, LCD, plasma, this kind of display has many advantages such as low cost, large size and so on. However, distortions and complex profile are the main problems of it.

Holographic projection system designed for free space propagation was reported in WO 2005059881, which has advantages like high light efficiency, small size, robustness, etc. over normal projectors.

The combination of these two technologies will make both of them quite different. By using holographic projection, it is possible to develop a simple triangle wedged waveguide as display, while this structure will cause band gaps and serious distortion in waveguide display by normal projecting. Holographic projection can take advantage of this simple wedged waveguide by correcting distortions and band gaps by holograms, instead of modifjing waveguide profile. The propagation of light in free space and inside the wedged waveguide is very different. Therefore, holographic projection system designed for these two purposes will be different.

This invention can be used in producing large screen, low cost, eco-friendly displays.

Brief Description

This invention includes an algorithm of generating holograms for the wedged waveguide panel, the wedged waveguide fit for that algorithm and apparatus for projecting holograms in the wedge waveguide.

Fig.1 shows the layout of the whole system, including the holographic projection system and wedge shape waveguide panel. The holographic projection system projects holograms, kinoforms with special calculation, into the waveguide. After propagation, they will be replayed as the target images on the screen.

Waveguide panel for holographic projection The waveguide panel 1 for holographic projection is wedged, and its side view is a simple triangle structure, as shown in Fig. 1. The vertex angle of the triangle is ci The waveguide has an input surface and one or two output surfaces. There is angle J between the input surface and the output surface.

The bottom part of the waveguide panel is the fan-out region, and the top part of the panel is the screen. Furthermore, the fan-out region can be folded to the back of the screen to save the space.

This profile is different from the waveguide display in W00172037. Firstly, its shape is wedged, but not tapered as described in W00172037. Wedged waveguide is useless for normal projection used in the previous patent, because it will cause serious distortions. However, holographic projection can eliminate these distortions by holograms themselves so that make the simple triangle wedge shape waveguide useful. Secondly, the position where rays leave the waveguide is decided by both its injecting angle and the injecting position on the input surface, rather than only decided by the injecting angle as W00172037 described. Moreover, the projection system in this invention is holographic projection. It projects holograms rather than normal images into the waveguide panel.

Holographic Projection The holographic projection system is comprised by laser sources, beam expanding and collimating optics, spatial light modulator, image expanding optics, and control and signal processing unit.

Light source For monochromatic displays, the source is just one laser (red, blue or green depends on needs) or LED. For colorful displays, there are three lasers (red, blue, and green, RGB) or LEDs in the system. The output power of these light sources is controlled by the control and signal-processing unit, which makes it possible to show images at the brightness required and save the power consumed by the whole system.

Synchronisation is always necessary for making the light sources synchronise with the holograms displayed on SLM.

Beam expanding and collimating optics Beam expanding and collimating optics are used for expanding and collimating beams generate by light sources. It may contain several lens, prisms, and other optic components.

Image expanding optics Image expanding optics is used for expanding images output by the SLM. It may contain several lens, prisms, polarizer, and other optic components. This optics may be integrated into the beam expanding and collimating optics with careful design.

Spatial Light Modulator (SLM) The Spatial Light Modulator is a device displaying holograms on it. It can be grating structures, photos, or electronic microdisplays, such as LCoS (Liquid Ciystal on Silicon) chips or (DLP) Digital Micro mirror Device, etc. When using LCoS chips, phase modulation (both binary and multi-phase modulation can be applied, depending on the SLM) is applied instead of amplitude modulation, which will significantly reduce the power steering into the zero order on the replay

field, thus greatly save the energy.

Control and signal processing unit This unit contains electronic devices and circuits.

This unit is responsible for synchronising the light source and the SLM by adjusting the power output of the light source. In addition, it is also responsible for synchronising three-color light sources (RGB) with the SLM for colorful application.

Control and signal processing unit is a kind of Application Specific Integrated Circuit (ASIC), which is also responsible for receiving signals and displaying holograms on the SLM. For the application in which holograms are calculated by external computers, this unit receives holograms and then directly transfers them to the SLM.

In the application that target images rather than holograms are sent to the holographic projection system, the control and signal processing unit may include Microprocessors, FPGAs or DSPs chips to generate holograms. Holograms will be transferred to the SLM after being generated. A new algorithm named Wedge Transform and Inverse Wedge Transform is applied to generate holograms in wedge waveguide panel. It is programmed into Microprocessors, FPGAs or DSPs chips mentioned above.

Wedge Transform and Inverse Wedge Transform Inverse Wedge Transform is used to generate holograms for the waveguide. It is comprised by the following steps: (1) Add phase for the input image; (2) Divide the screen into N several areas according to where rays with injecting angle within a range (for example, + 2a] leave the waveguide. , is an injecting angle, and a is the vertex angle of the waveguide.

(3) Fourier Transform or Inverse Fourier Transform the target image on the corresponding areas and keep the corresponding bands of the angular spectrum A(f,f) of the results respectively.

(4) Inverse propagate the results of step (3) A (f, A'(f,f) = A,2(fx,fy)xeisin2na1_(2J)_(2fY) , wherek = 2/2, A is the wavelength of the injecting ray.

(5) Reverse rotate A' (f f) by angle it / 2-2na, where a is the vertex angle of the wedge waveguide. (Since holograms are not very sensitive to the rotate angle, in many cases, this step can be passed over.) (6) Calculate and correct the distortion caused by injecting into the wedge interface and lens.

(7) Inverse Fourier Transform or Fourier Transform the result to get the corresponding amplitude and phase distribution. Then accumulate all areas of the amplitude and phase distribution to get the final hologram.

In the Inverse Wedge Transform described above, the sequence of step (1) and (2) can be exchanged. Steps (6) to (7) can be replaced by the following steps: a. Calculate and correct the distortion caused by injecting into the wedge interface b. Inverse Fourier Transform or Fourier Transform the result to get the corresponding amplitude and phase distribution, then accumulate all areas of the amplitude and phase distribution to get the final hologram.

c. Calculate and correct the distortion caused by lens.

The Wedge Transform is used to calculate how light propagates in the waveguide and can simulate a hologram's replay field (the target image) on the screen. It includes steps described below: (1) Inverse Fourier Transform or Fourier Transform the hologram to get its angular spectrum. Then divide it into several bands.

(2) Calculate and correct the distortion caused by injecting into the wedge interface and lens.

(3) Rotate the result of (2) by angle ir / 2-2na, where a is the vertex angle of the wedge waveguide. (Since holograms are not very sensitive to the rotate angle, in many cases, this step can be passed over.) (4) Propagate the results of step (3) A, (j, A' (f f) 7 Ls2na'-(j where k = 2 / A, A is the wavelength of the injecting ray.

(5) Fourier or Inverse Fourier Transform every band respectively, and just keep its amplitude and phase distribution in its corresponding area.

(6) Accumulate all areas of the amplitude and phase distribution to get the final image.

In the Wedge Transform described above, steps (1) to (2) can be replaced by steps below: a. Calculate and correct the distortion caused by lens.

b. Inverse Fourier Transform or Fourier Transform the hologram to get its angular spectrum. Then divide it into several bands.

c. Calculate and correct the distortion caused by injecting into the wedge interface.

In the Wedge Transform described above, the sequence of step (3) and (4) can be exchanged.

To improve the image quality, several steps described as following may be applied.

Firstly, Inverse Wedge Transform the input image to get the initial hologram.

Quantise it and then Wedge Transform the quantised hologram to get its amplitude and phase distribution on the screen (replay field). Throw the amplitude and keep the phase. Add the phase to the input image and then Inverse Wedge Transform the image with the new phase. Repeat steps described above after achieving the iterative number set. Afterwards, output the result to the SLM.

To further improve the image quality, a method that reducing noise and correcting distortions by displaying subframes of each image in time sequence can be applied.

Similar method is reported in W02005059881 and US20090322738. However, in this invention, the new algorithm Wedge Transform and Inverse Wedge Transform are integrated into this method, so it is different from the one in patents mentioned above.

The method has several steps: (1) Calculate the number of subframes that each image is comprised by, according to the hardware used, and record the number as M; calculate how many iterations should be applied to generate each subframe and record the number as N. (2) Add phase distribution to the image. Random phase can be set as the initial phase distribution.

(3) Inverse Wedge Transform the image and get the hologram (one subframe).

(4) Quantise the result of step (3) to get the subframe suitable for the SLM used.

(5) If all N iterations are finished, go to step (6); or else Wedge Transform the result of step (4) and take the phase of the result, then add this phase distribution to the original input image. Jump back to step (3).

(6) Display the subframe on the SLM.

(7) If all M subframes have been displayed, then go back to step (2) and display the next input image; or else Wedge Transforn1 the subframe displayed in step (6).

Compare the amplitude distribution of the result with the original image. Modify the image based on this result to compensate the distortion in the next subframe. Jump back to step (2).

Embodiments of the invention will now be described with reference to the drawings, of which: Fig. 1 is the side view of an example the holographic waveguide display.

Fig. 2 is the plan form of the example described in Fig. 1 Fig. 3 is another example of the holographic waveguide display.

Fig. 4 is the plan form of the example described in Fig. 3 Fig. 5 shows a block diagram of an embodiment of the holographic projection module for holographic waveguide display.

Fig. 6 shows a block diagram of another embodiment of the holographic projection module for the holographic waveguide display.

Fig. 7 shows an example hardware for holographic projection module, realising the function described in Fig 6.

Fig. 8 is the embodiment of holographic waveguide display, explaining the basic principle of the system.

Fig. 9 shows a block diagram of an embodiment of the algorithm named Inverse Wedge Transform, which is used to generate holograms for the waveguide.

Fig. 10 shows a block diagram of an embodiment of the algorithm named Wedge Transform, which is used to define how waves propagate in waveguide.

Fig. 11 shows an algorithm used to correct the distortion on the waveguide display's screen, in which the Wedge Transform and Inverse Wedge Transform are applied.

Application This invention includes a waveguide used as the screen and a holographic projection module. Referring to Fig. 1 to Fig. 4, these show two examples of holographic waveguide devices with the waveguide screen 11 and holographic projection module 12. As shown in Fig. 1, the shape of the waveguide is triangle, and its vertex angle is ci. The top part can be cut to save materials, so the waveguide is wedged. The bottom surface where light inject into the waveguide can be tilted. The angle between it and screen surface of the waveguide is f3. The plan form of it can be square, triangle or another shapes. The bottom half of the waveguide can be used as the fan- out region 111, and the top half of the waveguide is used as the screen 112. The fan-out region can be folded back to the screen to save the space, as shown in Fig. 3 and Fig. 4. It need coating the back or screen surface (or both of them) of the waveguide to make light only eject the waveguide at its screen surface but not the back surface.

One important difference between the waveguide in this invention and the waveguide reported in patent WOO 172037 is that the waveguide in this invention is wedged but not tapered.

As shown in Fig. 5 and Fig. 6, the holographic projection module is comprised by the following modules: Light Source: coherent light sources are used here, such as laser diode or LED. Three monochromatic light sources, including red, green and blue light can be combined together in the system to display colorful images.

Beams expanding and collimating module: This module is used to expand and collimate beams generated by the light source. It also includes the image expanding optics, which is used to expand and collimate the output beams of the SLM to display the target image.

Spatial Light Modulator module: this module is used to modulate the amplitude or phase distribution of the injecting beams. Liquid Crystal on Silicon (LCoS) chips, Digital Micro Mirror Device (DMD), gratings, or even holographic films can be used as the spatial light modulator. If LCoS or DMD chips are used, then holograms shown on it can be swiftly changed under the control of electronic devices, thus the system can display videos.

Control and signal processing module: The control and signal processing module is used to control the beams generated by the light sources. It is Application Specific Integrated Circuit (ASIC) comprised by electronics with microprocessor. If the spatial light modulator module uses digital devices like LCoS or DMD, then the control module should have the function to control the holograms showing on it and synchronise them with the light source.

If the input image is the target image, then this module should have the function to transfer the image into holograms. Tn other words, the hologram generating function is integrated into this module. If the system is designed for only receive holograms, thcn the control and signal processing module will directly show received holograms on the SLM and synchronisc them with light source. In this case, the hologram generating function can be carried out by external computers.

Fig. 7 is a hardware example of the embodiment described of holographic projection module. The light source in this example is comprised by a red, a green and a blue laser. The beam expanding and collimating module is comprised by lens 1 to 5 and two prisms. Lens 1, 2, 3 are responsible for expanding and collimating the injecting laser beams. Lens 4 and S expands output images. A reflective LCoS chip is applied here as the SLM. It modulates the injecting light by phase with a polarizer. A DSP or FPGA chip is used here as the core of the control and signal processing module. It transfers the input image to holograms simultaneously, then displays it on the SLM and synchronises it with the light source.

There are many ways to realise the scheme shown in Fig. S or Fig. 6. Fig. 7 is just one example of it. Tt can also be realised by systems using three SLMs. For example, the red, green and blue laser sources illuminate three LCoS chips respectively, and optics can be used to combine the output of these three LCoS chips to form the final image.

This can further increase the image quality.

The light propagation in waveguide is different from what it does in free space.

Therefore, the algorithm of generating holograms in waveguide is different from that in free space. The wedged waveguide is used in this invention. Beams injecting with different angles can be categorized into several bands. The model is that each band of beams are rotated an angle and then projects onto the screen. Fig. 8 shows the how this model works. It is a plan form of a wedged waveguide. Coating is applied on its surface. Its vertex angle isa, its height is H, length is L, and the injecting angle is 0. After calculation, it is proved that the propagation of beams with injecting angle between (O, Q + 2a] is equal to that they are rotated by 2ma, and then project onto thc screen surface; the propagation of beams with injecting angle between (O -2a, O] is equal to that they are rotated by 2(m + 1)a, and then project onto the screen surface; Fig. 9 shows an algorithm of how to generate holograms for the waveguide, which is named Inverse Wedge Transform in this invention. It is comprised by the following steps: (1) Add phase D(x,y) for the input image T(x,y). The result is T(x,y)xe'4.

The initial phase may use random distribution.

(2) Divide the screen into N areas (areas can be partly overlapped), according to where the different injecting angle leaving the waveguide. These N areas are corresponding to the N bands in angular spectrum respectively.

T(x,y) = T(x,y)xe' xP(x,y), where (x,y)is a filter.

1 (x,y)eR I (x, y) = { , R is the corresponding area on the screen 0 (x,y)R (3) Fourier Transform or Inverse Fourier Transform the target image in the corresponding area n to get its angular spectrum. Only keep the corresponding bands of the angular spectrum of the results respectively.

A(f,f) =F{](x,y)}xQ(f,f) ,where F{} is Fourier Transform (or Inverse Fourier Transform, depends on systems). Q(ff) is a filter for angular spectrum.

1 (f f)eS Q = (L: f) , where S, is the angular spectrum band corresponding to the area ii.

(4) Inverse propagate A(ff).

A'(f f) A(j, ejsin(2na 1_, where k = 2/A, A is the wavelength of the injecting ray, and L is the distance between the injecting surface and the vertex of the triangle waveguide, as shown in Fig. 8.

(5) Reversely rotate A'(f,f) by angler/2-2na, where a is the vertex angle of the wedge waveguide. (Since holograms are not very sensitive to the rotate angle, in many cases, this step can be jumped.) (6) Calculate and corrcct thc distortion causcd by thc wedge interfacc and lcns.

(7) Inverse Fourier Transform or Fourier Transform the result to get the amplitude and phase distribution of every band in its corresponding area, then accumulate all areas of the amplitude and phase distribution to get the final hologram.

The sequence of the steps described above can be changed to fit for different systems.

Phase or amplitude distribution should be chosen to be quantised to generate holograms. For example, for binary phase spatial light modulator, one quantise algorithm is make all the phase big tan 0 to be in 2, and others to be in/ 2 to get a binary phase hologram.

In mathematics, step 3, 4, 6 can be expressed as: F' {F{T(x, y) x x (x, y)} x x e/hl2n 1_(2J2_(2J)2 = [T(x, y) x x (x, y)] * F'{Q x e1 mn2nl(2 (2J) js2,a1-(Af)2-(Af)2 where * is convolution operator. For the reason that F xe} is independent with the input image, it can be calculated and stored before generating holograms. We can use one convolution calculation to replace two Fourier Transform jkLsin2na1_(2fx)2_(2fy calculation, and with the pre-stored F x e}, it can fasten the computing speed.

Furthermore, the above algorithm is reversible. With slightly modification, we can get the Wedge Transform, which defines how injecting light propagates in a wedged waveguide. Fig. 10 shows the Wedge Transform. It is comprised by the following steps: (1) Inverse Fourier Transform or Fourier Transform the hologram to get its angular spectrum. Then divide it into several bands.

(2) Calculate and correct the distortion caused by wedge interface and lens.

(3) Rotate results of (2) by angle it / 2 -2na respectively, where a is the vertex angle of the wedge waveguide. (Since holograms are not very sensitive to the rotate angle, in many cases, this step can be passed over.) (4) Propagate the results of step (3) A (f, A' (f f) = u' e_J rn2n1(2j)1 -(f)2 where k = 2it / A, 2 is the wavelength of the injecting ray, and L is the distance between the injecting surface and the vertex of the triangle waveguide, as shown in Fig. 8.

The sequence of the above steps can be changed to fit different systems.

The quantise process causes noises. To improve the image quality, a desired image can be showed by several holographic subframes so that temporal averaging amongst subframes to reduce the perceived noises. This is based on the principle that if the subframes are displayed fast enough, they would be integrated together in the human eye. This is similar to the method described in patent US 20090002787 and WO 2005059881, but they are different because our one is based on the wedge transform developed for projection in waveguide. Our method is comprised by the following steps: (1) Input one new image. Set the number M, which means how many subframes will integrate together to form the image.

(2) Add phase distribution to it. (The initial phase can use random distribution) Set the number N, which means the iterative times that a subframe will be calculated before displayed on the SLM.

(3) Carry out the thverse Wedge Transform to generate the hologram.

(4) Quantise the hologram according to the parameter of the SLM used.

(5) If N iteration is finished, jump to step (6); or else carry out Wedge Transform to get the amplitude and phase distribution of the replay field of the quantised hologram.

Keep its phase distribution as the distribution used in step (2). Jump back to step (2) (6) Display one subframe on the SLM.

(7) If all the subframes have already been displayed, then input a new image and jump back to step (1); or else carry out the Wedge Transform to get the amplitude and phase distribution of the replay field of the quantised hologram, and comparing the amplitude distribution with the target image. Use the comparison results as the feedback to modifi the input image, and then jump back to step (2).

Claims

Claims 1. An optical system including a waveguide screen (11) and a holographic projection system (12); The waveguide has a light input surface and output surface. The position where the ray leaving the waveguide is decided by the combination of its injecting angle and injecting position.
2. An optical system according to claim 1, in which the waveguide is wedged so as to narrow along its direction of propagation.
3. An optical system according to any of claims 1-2 and further including an optical diverter allowing the fan-out region (HI) folded over the screen (112).
4. According to claim 1, the holographic projection system for waveguide described in claims 1 to 3, which comprises light sources, spatial light modulator.
5. The holographic projection system according to claim 1 and 4, which comprises a collimation optics to collimate said light for spatial light modulator, and projection optics.
6. The holographic projection system according to claim 1 and 4, which comprises a control module controlling the light source and its output power.
7. The holographic projection system according to claim 1, 4 and 6, wherein said a digital signal processor module is configured to receive input digital data and transfer it to the SLM.
8. The holographic projection system according to claim 1, 4, 6 and 7, wherein said a digital signal processor module is configured to generate holograms for SLM based on the input images.
9. A method generating holograms for waveguide described in claim 1 to 3, which comprises an algorithm named Inverse Wedge Transform comprised by the following steps: (1) Add phase for the input image; (2) Divide the screen into several areas according to where the rays within the same injecting angle band leaving the waveguide.(3) Fourier or Inverse Fourier Transform the target image on the corresponding areas and keep the corresponding bands of the angular spectrum of the results respectively.(4) Propagate the results of step (3) A,, (j., f) respectively by multiply a factor. The result after propagate will be A,,'(f,f)= wherek = 2,r/A, A is the wavelength of the injecting light and n relates to the corresponding band of area n (5) Reverse rotate A(f,f) by angle r/2 -2na, where a is the vertex angle of the wedge waveguide.(6) Calculate and compensate the distortion caused by light injecting into the wedge interface and lens.(7) Inverse Fourier Transform or Fourier Transform the result to get the corresponding amplitude and phase distribution. Then accumulate all areas of the amplitude and phase distribution to get the final hologram.
10. A method generating holograms for waveguide described in claim 1 to 3, based on claim 9, with step (5) being jumped.
11. A method generating holograms for waveguide described in claim 1 to 3, based on claim 9 or 10, with step (1) and (2) being swapped.
12. A method generating holograms for waveguide described in claim 1 to 3, based on claim 9 or 10 or 11, with step (6) and (7) being replaced by the following steps: a. Calculate and compensate the distortion caused by light injecting into the wedge interface.b. Inverse Fourier Transform or Fourier Transform the result to get the corresponding amplitude and phase distribution. Then accumulate all areas of the amplitude and phase distribution to get the final hologram.c. Calculate and compensate the distortion caused by lens system.
13. A method calculates how waves propagate in the waveguide described in claim 1 to 3, which comprises an algorithm named Wedge Transform comprised the following steps: (1) hverse Fourier Transform or Fourier Transform the hologram to get its angular spectrum. Then divide it into several bands.(2) Calculate and correct the distortion caused by light injecting into the wedge interface and lens.(3) Rotate the result of (2) by angle r / 2-2na, where a is the vertex angle of the wedge waveguide.(4) Propagate the results of step (3) A(f,f) A(f, f) = A12(f., f)x e_J in2naV1_(kt)1-(Af)2, where k = 2/2, 2 is the wavelength of the injecting ray.(5) Fourier or Tnverse Fourier Transform every band respectively, and just keep its amplitude and phase distribution in the corresponding area.(6) Accumulate all areas of the amplitude and phase distribution to get the final image.
14. A method calculates how waves propagate in the waveguide described in claim 1 to 3, based on claim 13, with step (3) being jumped.
15. A method calculates how waves propagate in the waveguide described in claim 1 to 3, based on claim 13 or 14, with step (1) and (2) being replaced by the following steps: a. Calculate and compensate the distortion caused by the lens system.b. Inverse Fourier Transform or Fourier Transform the hologram to get its angular spectrum. Then divide it into several bands.c. Calculate and compensate the distortion caused by injecting into the wedge interface.
16. A method calculates how waves propagate in the waveguide described in claim 1 to 4, based on claim 13 or 14 or 15, with step (3) and (4) being swapped.
17. A method reducing noise of holographic images shown on the waveguide described in claim 1 to 4, which applies the Wedge and Inverse Wedge Transform. It comprises the following steps: (1) Input one new image. Set the number M, which means how many subframes will integrate together to form the image.(2) Add phase distribution to it (The initial phase can use random distribution). Set the number N, which means the iterative times that a subframe will be calculated before displayed on the SLM.(3) Carry out the Inverse Wedge Transform to get the hologram.(4) Quantise the holograms according to the parameter of the SLM used.(5)If N iteration is finished, jump to step (6); or else carry out Wedge Transform to get the amplitude and phase distribution of the replay field of the quantised hologram.Keep its phase distribution as the phase distribution used in step (2). Jump back to step (2).(6) Display one subframe on the SLM.(7) If all the subframes have already been displayed, then input a new image and jump back to step (1); or else carry out the Wedge Transform to get the amplitude and phase distribution of the replay field of the quantised hologram, and comparing the amplitude distribution with the target image. Use the comparison results as the feedback to modifSi the input image, and then jump back to step (2).