JP6951738B2 - Hologram data creation program and hologram data creation method - Google Patents

Description

The present invention relates to a hologram data creation program and a hologram data creation method.

Holograms produced by holographic technology are extremely useful in various fields such as three-dimensional displays, special optical elements, large-capacity memories, and security.

On the other hand, in the holographic technique for producing a hologram, a light wave from a three-dimensional object or an image is calculated, and the Sommerfeld diffraction integral, the Fresnel diffraction integral, or the like is used for the calculation of the light wave.

By the way, in the above integral calculation, a method using a fast Fourier transform can be considered.

For example, the propagation source, considering the case where the diffraction calculation between surfaces of N × N pixels in the propagation destination both calculating the integral, the amount of calculation increases in proportion to N ^4. For example, when N = 2048, it takes about one hour even when a general computer is used. On the other hand, when the fast Fourier transform is used, the amount of calculation can be reduced to ^{N 2 log N.} That is, in the case of the above N = 2048, it can be shortened to about 1 second.

However, the calculation of light waves by the fast Fourier transform can only calculate the light wave propagation between planes, and as a result, it is necessary to use the fast Fourier transform multiple times to obtain the three-dimensional distribution of light waves. , The above time is not short enough.

Therefore, in view of the above problems, an object of the present invention is to provide a hologram data creation method and a hologram data creation program capable of further shortening the calculation time.

The hologram data creation program according to one aspect of the present invention, which solves the above problems, performs a wavelet transform on a computer to obtain wavelet region data, a step of selecting a part of the wavelet region data, and a selected part. This is to execute the step of performing the inverse wavelet transform on the wavelet region data of.

Further, the hologram data creation method according to another aspect of the present invention includes a step of performing a wavelet transform to obtain wavelet region data, a step of selecting a part of the wavelet region data, and a part of the selected wavelet region data. It is provided with a step of performing an inverse wavelet transform on the data.

As described above, according to the present invention, it is possible to provide a hologram data creation method and a hologram data creation program that can further shorten the calculation time.

It is a figure which shows the example of the distribution of the wavelet coefficient. It is a figure which shows the example of PSF. It is a figure which shows the example of the calculation result of the wavelet decomposition of PSF. It is a figure which shows the example of PSF. It is a figure which shows the strength profile in the example of FIG. It is a figure which shows the example of the hologram created in an Example. It is a figure which shows the example of the hologram created in an Example. It is a figure which shows the example of the hologram created in an Example.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. However, the present invention can be implemented in many different embodiments, and is not limited to the specific examples in the embodiments and examples shown below.

The hologram data creation program (hereinafter referred to as “this program”) according to this embodiment is
The step of (S1) performing wavelet transform on the computer to obtain the wavelet region data, (S2) the step of selecting a part of the wavelet region data, and (S3) repeating the above (S1) and (S2) a plurality of times, respectively. In (S4), a step of adding up a part of the selected wavelet region data and a step of performing an inverse wavelet transform on the selected part of the wavelet region data are executed.

Although not limited, this program can be realized by being recorded in an information processing device, that is, a recording medium such as a hard disk of a computer or a CD-ROM, and executed. More specifically, a central computing device (CPU), a non-volatile storage device such as a hard disk or a flash memory, a volatile storage device such as a RAM, a bus line for electrically connecting these, a keyboard, a mouse, etc. A computer equipped with an input device, a display device such as a liquid crystal display, or the like is used, the program is stored in the non-volatile storage device, and the desired process can be executed by reading and executing the program in the volatile storage device. ..

That is, as is clear from the above description, by executing the above program, (S1) a step of performing wavelet transform to obtain wavelet region data, (S2) a step of selecting a part of the wavelet region data, (S3). ) The steps of repeating the above (S1) and (S2) a plurality of times and adding a part of the selected wavelet area data in each step, (S4) inverse wavelet for the selected part of the wavelet area data. It is possible to provide a hologram data creation method (hereinafter referred to as "the present method") for executing the step of performing the conversion. The details of this method will be described below.

In principle, the calculation of light waves can be thought of as the addition of light waves emitted from a point light source, and this method significantly reduces the amount of calculation for light wave calculations by performing this addition of light waves in the wavelet transform region. be able to.

First, this method includes a step of performing (S1) wavelet transform and obtaining wavelet region data. This step is a so-called pre-calculation.

In this step, the point spread function (PSF) u _zj (x _h , y _h ) is calculated from the object point (0, 0, z _j ), and then the PSF in the spatial region is converted to the PSF in the wavelet region. In this case, the wavelet transform is preferably a fast wavelet transform.

Here, PSFu _zj (x _h , y _h ) is expressed as follows using the scaling coefficients s ^(l) _{m and n.} Note that l means the level of wavelet decomposition.

Further, in the above equation, m and n are integers, and φ means a scaling function, respectively.

If the level of the scaling coefficient is zero, it can be considered as the original signal. That is, the following is satisfied.

Also, wavelet transform, as represented by the following formula, u zj (x h, y h) a scaling factor s (l) m, n and wavelet coefficients w (l) LH, m, n ', w ( l) Decompose into HL, m, n' , w (l) HH, m, n'.

In this method, it has been empirically confirmed that a high quality image can be obtained when l is 2 or less, but is not limited, and is preferable, depending on the values of m and n. different.

Here, regarding the distribution of the scaling coefficient and the wavelet coefficient after the wavelet transform, FIG. 1 shows an example of PSF in FIG. 2, and FIG. 3 shows an example of the calculation result of the wavelet decomposition of this PSF. In these figures, the pixel pitch was 10 μm and z _j = 100 mm at a wavelength of 633 nm. The original number of scaling coefficients and wavelet coefficients was the same as the number of pixels of the hologram, and was set to N _h ² .

By the way, in the step of adding together, which will be described later, if the numbers are added as they are, the amount of calculation becomes enormous. Therefore, this method includes (S2) a step of selecting a part of the wavelet region data. Specifically, among the data obtained in the wavelet transform performed in (S1) above, only the data having a large wavelet coefficient is selected. This step is also performed as part of the pre-calculation.

In this step, the step of selecting a part can be appropriately adopted as long as the amount of calculation can be reduced, but it is performed by deleting the one having a small wavelet coefficient (leaving the one having a large wavelet coefficient). The magnitude of this coefficient is preferably evaluated and selected based on the amplitude.

In addition, in this step, the following _Nr coefficient is defined and a part is selected in order to reduce the amount of calculation. In the following equation, W _j ² is _{the radius of PSFu zj} , r means the selectivity, and means how much to select from the one having the largest amplitude.

This effect is clear from the description described later. For example, when the number to be selected is r = 1%, the amount of calculation is 1/100.

Further, coefficient selected is preferably, for example, to record by the vector v _z are defined below.

In the above equation, α _{z and k} are expressed as follows.

Further, this method includes a step of repeating (S3) above (S1) and (S2) a plurality of times as described above, and adding a part of the selected wavelet region data in each of the steps. In other words, a plurality of wavelet region data are obtained by repeating the above (S1) and (S2) a plurality of times, and by adding these, the wavelet region data after the addition is obtained.

In this step, specifically, (S1) and (S2) obtain a plurality of planar PSFs by making the heights (z) of the object points different from each other, perform wavelet transform for each of them, and further, respectively. This is done by selecting some wavelet region data and adding them together.

Here, the addition is not limited, but is preferably performed based on the following formula.

Here, δ (m, n) is a Dirac delta function. Further, in the above equation, the coefficients _{cz, k at} the position (m, n) are shifted in the horizontal direction and the vertical direction according to the following equation in superposition, and are added to the wavelet space ψ (m, n). Will be done. Note that x ₁ and y ₁ mean the coordinate positions of the object points initially calculated (before the shift), respectively.

In addition, in the above-mentioned addition formula, addition means _{czj, k in the same region.} For example, in FIG. 1, if c _zj of the point _{a, k} is moved to a point b, while performing adjustment adding, if the point a is moved to c or d, does not perform adjustment added. This is because a and b are the same region, and a and c and a and d are different regions.

Further, (S4) includes a step of performing an inverse wavelet transform on a part of the selected wavelet region data.

In the "inverse wavelet transform" of this step, the inverse transform of the same transformation as the wavelet transform used in the above (S1) can be used.

Note that the original PSF was used in FIG. 4 (a), the PSF obtained by using this method under the condition of r = 20% in (b), and the PSF obtained by using this method under the condition of r = 10% in (c). The PSF obtained by using this method under the condition of r = 5% is shown in (d), respectively.

Further, in FIG. 4 (e), the diffraction pattern obtained from the two object points is shown in (f), and the diffraction pattern obtained by using this method with respect to (e) under the condition of r = 20% is shown in (g). ), The diffraction pattern obtained by using this method with respect to (e) under the condition of r = 10% was obtained with respect to (h) using this method with respect to (e) under the condition of r = 5%. The diffraction patterns are shown respectively.

Further, FIG. 5 (a) shows the intensity profiles of FIGS. 4 (a) and 4 (d), and FIG. 5 (b) shows the intensity profiles of FIGS. 4 (e) and 4 (h), respectively.

By executing each of the above steps, in this method, for example, when r = 1%, the amount of calculation can be further reduced to about 1/100 as compared with the case where a normal fast Fourier transform is performed. Become. That is, it is possible to speed up the calculation of light waves while maintaining the image quality. That is, it is possible to provide a hologram data creation method and a hologram data creation program that can further shorten the calculation time.

Here, the effect of the present invention was actually confirmed by using a specific example of the above method. Specifically, conventional methods (SC Kim et al., “Effective generation of digital holography Off three-dimensional objects using a novel using a look-up table”, App2, App2, App. , The difference from the above method (r = 5%, r = 1%) was confirmed.

In this embodiment, three types of images (10,000 object points, 100,000 points, and 1 million points) are used, and z = 0.5 m, 0.2 m, 0.1 m, and 0.05 m, respectively. The effect of the above method was confirmed for each of them. Among these results, the results of z = 0.5 m and 0.05 m are shown in FIGS. 6 to 8. The results of these calculations are shown in Tables 1 to 3 below. In this case, the size of the hologram was set to 2048 × 2048 pixels.

According to this result, it was confirmed that the PSNR of each method was about 30 dB, which was within the range that is said to have no problem in image processing. It was also confirmed that the calculation time was significantly reduced compared to the conventional technology, although it depends on the distance and shape between the three-dimensional objects.

The present invention has industrial applicability as a hologram data creation program and a hologram data creation method.

Claims (4)

On the computer
A step of obtaining wavelet region data by performing a wavelet transform that transforms the point spread function (PSF) of the spatial region into the PSF of the wavelet spatial region.
The step of selecting only the wavelet region data having a large wavelet coefficient,
A step of adding only the selected wavelet area data moved to the same area.
A hologram data creation program for executing a step of performing an inverse wavelet transform on the wavelet region data after addition. Obtaining the wavelet domain data to PSF obtained by varying the height of the object point, and, according to claim 1, large only repeating plurality of selecting performs the wavelet coefficients of said wavelet domain data Hologram data creation program. A step of obtaining wavelet region data by performing a wavelet transform that transforms the point spread function (PSF) of the spatial region into the PSF of the wavelet spatial region.
The step of selecting only the wavelet region data having a large wavelet coefficient,
A step of adding only the selected wavelet area data moved to the same area.
A hologram data creation method comprising a step of performing an inverse wavelet transform on the wavelet region data after addition. Obtaining the wavelet domain data to PSF obtained by varying the height of the object point, and, according to claim 3 in which a plurality repeatedly performing steps to select only large wavelet coefficients of said wavelet domain data How to create hologram data.

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