Synthesize of a kinoform for CGH reconstruction using angler spectrum method

In this paper, we describe a Synthesize of a kinoform for CGH reconstruction using angler spectrum method. A hologram is a medium on which interference fringes of light are recorded. It is expected not only to represent three dimensions but also to be applied in various applications such as storage. Among them, the method of calculating by using phase is called kinoform. This method is suitable for optical reconstruction because of high light utilization efficiency


Optical hologram and Computer Generated Hologram(CGH) 1.1 Holography
The technique of projecting a three-dimensional image in space is called holography.Information recording the amplitude and phase information of the light emitted from the object is called a hologram.This recording and reconstruction uses light interference and diffraction.The three-dimensional image reconstructed by the hologram is the light itself emanating from the object, which can be perceived stereoscopically.When the observer moves, you can reconstruct the image from that angle.

Optical hologram
This chapter explains recording and reconstruction methods in optical holograms

Computer Generated Hologram(CGH)
CGH calculates the distribution of the interference fringes of the hologram by computer by propagating light.In the optical hologram, it is a problem that the recording process requires very high precision, but in CGH the distribution of the hologram can be obtained only by inputting data.Also, it is possible to generate a hologram of a virtual object that does not exist.
Since CGH calculates using discrete values, it is difficult to obtain a clear reconstructed image.In this research, the purpose is to reduce the error of the reconstructed image.Also, since the computational complexity of three-dimensional recording and reconstruction becomes enormous, consideration is made using a two-dimensional image

2.1
angular spectrum method There are several methods for finding the distribution of the hologram, but in this research we use the angular spectrum method.It is an advantage that the angular spectrum method does not suffer from constraints by distance, and the calculation is fast by FFT.The angular spectral method is performed using two Fourier transformations as shown in equation ( 1)

Recording and reconstruction of hologram in kinoform
Kinoform is a type of hologram recording phase.In the complex amplitude hologram, both the amplitude and the phase are recorded, but in the case of the kinoform, the amplitude is calculated as a constant value when the hologram is recorded.This makes the reconstructed image blurred in kinoform.Consider the method to reduce this error by the method described below.

Iterative dummy area method 3.1 Dummy area method
A dummy area method is one of error reduction methods in CGH.This is a method of adding a region where initial values of amplitude and phase are zero around the original image.The added region can take an arbitrary value (freedom of amplitude and phase can be used), thereby making it possible to reduce the error of the reconstructed image.

Problem of conventional dummy area method
The dummy area method is equivalent to increasing the size of the original image.This also increases the size of the hologram.Data of the hologram is output to a highresolution printer, a spatial light modulator, or the like.The size of the hologram depends on the output device.Therefore, it is not desirable to increase the size of the hologram Fig. 3.2 conventional dummy area method.

Proposed dummy area method
In the proposed method, we stop using the whole area of the enlarged hologram for reconstruction.Cut the dummy area part of the hologram and use the hologram of the size of the original image before adding the dummy area for reconstruction.However, this method increases the error of the reconstructed image.This is because the dummy area in the hologram also contains information on the original image.
When this method is used for kinoform, large error occurs.I will explain this F image as an original image.If the dummy area in the hologram is cut and reproduced, a large error occurs Fig. 3.4 reconstructed image using proposed method Since the information of the original image is also included in the cut portion, an error occurs.

Iterative dummy area method
Iterative dummy area method is a method for reducing hologram error.This method is used for kinoform which reconstructs by cutting the dummy area which is the proposed method.It has been confirmed that this method can reduce errors in complex amplitude hologram using angular spectrum method.

Fig. 3.5 Iterative dummy area method
As shown in Fig. 3.5, we adopt a method adding cuts of dummy areas proposed for iterative algorithm.

Simulation result
It shows the reconstructed image of the hologram recorded by the iterative algorithm using the same original image as in Figure 3.4 The reconstructed image is the result of 1000 iterations using dummy area eight times the size of original image.In normal kinoforms, large errors occur unless calculations are performed using large size dummy areas.Next, a simulation result of a reconstructed image in the case of using twice the dummy area of the original image is shown.It was found that there was no large difference in the reconstructed image using the dummy area of 2 times and 8 times of the original image.Such a result was also obtained when this method was used for a complex amplitude hologram.

Conclusions
We found that the proposed dummy area method in kinoform using angular spectrum method is effective.This made it possible to reduce the error without changing the size of the hologram.