JPS6053843B2 - How to form a pseudorandom diffuser plate - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION An object of the present invention is to improve the pseudo-random diffuser described in Japanese Patent Application No. 52-65007, and to obtain a high-density recording hologram from which a high-quality reproduced image can be obtained.

The pseudorandom diffuser proposed in the above Japanese Patent Application No. 52-65007 has six phase values of 0, π13,
2 whose constituent elements are 213π, π, 413π, and 513π
Dimensional phase sequence (φ(m, n)), m=1, 2, 3,...
..., M, , n = 1, 2, 3, ..., N, the partial phase sequence composed of φ (m, n) where both 1m and n are odd numbers is 0, It is determined by the arrangement of groups of 2'3π and 413π, and the difference between each address and the phase values at its nearest four addresses (top, bottom, left, and right) in the partial phase sequence is +213π is -213π (however, (Positive and negative signs appear with almost equal probability), each row or each column is a different phase sequence, and φ(M, n) where only one of 2m or n is an odd number is considered in all sequences. The vectorial average value of the phase values on both sides or above and below the address (hereinafter simply referred to as the average value; for example, the average value of (413π, 0) is equal to the average value of (413π, 2w), which is 513tr
shall be.

), and φ(M, n), where both 3m and n are even numbers, is πI in absolute value from the phase value on both sides of the address considered in the entire series.
The following method has been studied to embody a phase sequence that has four conditions: that the phase sequence is at the top and that the sum of the six phase values as a whole of the four-phase sequence is approximately equal. An example of this will be explained with reference to FIG. In Figure 1, (1) φ(1,1) is assigned one of 0,213π, 413π, and generally φ(1,2r1″+1) is
N-1φ(1,2
r1''-1) (where n''=1, 2, . . . , completed) plus +213π or -213π selected with equal probability, and create a series of odd addresses in the first row. However, 0
−213π, 413π+213w=0, (Ii)
Next, moving to the third line, φ(3,1) is the value of φ(1,1) plus +213π or -213π of the above condition, and generally φ(3,2r1″+1) is φ(1 , or ″+1) and the difference between φ(3, 2r1″−1) are both set to values whose absolute values are 213j.Here, φ(1, 2n″+
If 1) and φ(3,2n″-1) are equal, add +213π or -213π of the above condition to φζ(1,2n″+1), and if they are different, add one of 0.213π, 413π Let the remaining value be the value. In this way, the odd values in the third row are created. Sequentially in the same way, φ(M, n
), (Iii) φ(M, n) where only one of m or n is an odd number: . When m is an odd number and n is an even number, the average value of the phase values on both sides of each address is used, and when m is an even number and n is an odd number, the average value of the upper and lower phase values is used. However, the average value of 0 and 413π is 513π, (■) M,
For n co-even φ(M, n), φ(M, n-1)
If the values of and tφ(M, n+1) are equal, φ(M, n−
1) plus FrI3 or -π13 selected with equal probability; if different, use their average value. However, the average value of Wl3 and 513π is set to 0. If we construct a phase series under these conditions, we can obtain something like the one shown in Figure 2 (however, the phase value is normalized by π13)
. This 6-level composite pseudo-random phase sequence has certain quirks.

As shown in Fig. 3, the shading pattern corresponding to Fig. 2,
A chain of the same phase value from the upper right to the lower left is relatively common. Figure 3 shows each phase level (0, π'3
, 213π, π, 413π, 513π) are associated with different symbols to show the peculiarities of the arrangement. This habit is caused by the construction process mentioned in 2 above, and both M and n are odd numbers φ(
This can be clearly seen by examining the probabilities that M, n) take the respective values of 0, 213π, and 413π. φ(M, n) (where M
, n are odd numbers) become 0,213π, 413π respectively as PO(M,n), P2(M,n), P4(M
, n), then if m = 1 and n ~ 1, if n = 1 and m ~ 1, if m ~ 1, n ~ 1, then "---7--" expressed.

Table 1 shows each probability when φ(1,1)]=0.

The following can be seen from Table 1. P2 and P4 at odd addresses for all M and b are the same value, and unlike PO (as is clear from equations (1), (2), and (3)), even if M and n become large, PO and P2 are not very close values.
That is, 213π and 413π occur with the same probability at each address, but only 0 always differs. Also, diagonally,
The line PO>P2=P4 and the line PO>P2=P4 appear alternately. More importantly, M,n
Both odd numbers and arbitrary φ(m-2, n-2) are 0,213
If the phase value reaches a certain phase value among π, 413π, φ(M, n) at the lower right corner has a high probability of becoming φ(m-2, n-2).
It has the same phase value as . This is proved as follows. If we now set φ(m-2, n-2) = 1π, we can say that.

Therefore, by using equation (3), it can be seen that P4 is larger than PO and P2.

These are the causes of the habit appearing in Figure 2. Such sequence quirks directly affect the hologram and, in turn, have an equally negative effect on the quality of the reconstructed image. The present invention provides a diffuser plate having a phase sequence that eliminates the above drawbacks.

The present invention will be described in detail below with reference to the drawings.

First, a configuration example of the present invention will be explained with reference to FIG. 1 and FIGS. 4 to 6. Note that the phase sequence construction process (1), (Ii), (Iii), and (Iv) described above differs only in (11), and everything else is the same.
Therefore, only the process (Ii) will be explained here. (1) ``Same as (1) above. (Ii)'' Next, move to the third line φ (3, N) and n = N, N-2, N-4, .
. , 3, 1 in the order of φ(3, n).

Now, φ(3, N) is the value of φ(1, N) plus +213π or -213π, which appear with equal probability, and generally φ(3
, or ″-1) is the difference between φ(1, addition″-1) and φ(3,
2r1''+1), the absolute value of both of which is 213π.Here, φ(1,2n''-1) and φ(3,
2n″+1) are equal, then 213π or − of the above condition
Add 213π to φ(1, Nod''-1), and if they are different, use the remaining value within 0,213w,413π.In this way, create the odd address in the third row and add the following 5 In the row, φ(5,
Determine n). That is, φ(5,1) becomes φ(3,1
) plus the above condition 213π plus -213π,
Generally, φ(5,2r1″+1) is φ(3,2n″+1)
The absolute value of both the difference between
The convention for determining φ(5, 2n″+1) by the relationship between φ(5, 2n″−1) and φ(5, 2n″−1) is the same as above. , 13,..., m=1, 3, 5, 7,..., N-2, N in the order of m=
Each row of 3, 7, 11,... is n=N, N-2,...
φ(M, n) is determined in the order of 3 and 1. (Iii)'' Same as (Iiii) above.

(Iv)'' Same as (Iv) above.

The phase series constructed in this way is shown in FIG. 4, and FIG. 5 shows a diagram of FIG. 4 (however, the phase value was normalized to 113W) as a grayscale pattern.

Similarly to FIG. 3, FIG. 5 also shows the peculiarities of the arrangement by associating different symbols with each phase level in FIG. 4. Furthermore, as in this embodiment, each even row and each even column is a 6-level pseudorandom sequence in which the difference between adjacent phase values is +π13 or -π13 selected with equal probability, and all Even when considered in the phase series, the difference between the phase value of each address and the phase values on both sides is jl thicker in absolute amount. Furthermore, since both M and n of φ(M, n) are determined by folding the odd partial phase sequences in a zigzag pattern, the arrangement pattern L shown in Figure 3 is not seen in Figure 5. . Figure 5 does not have the same quirks as in Figure 3. PO (M, n), P2 (M, n), P4 (M,
n) is n=1 and m=4m″+1 (m′=1,2,73,...
PO(M,l)=↓(P2(m-2,1)+
P4(m-2,1)) P2(M,l)=b(P4(m-2,1)...(7)
+PO(m-2,1))P4(M,l)=A(PO(
m-2,1) +P2(m-2,1)) When n=N and m=4m'-1, PO(M,N)=h(P2(m-2,N)+P4(m-
2, N)) P2 (M, N) = Mu (P4 (m-2, N)..., 8)
+PO(m-2,N))P4(M,N)=b(PO(m
-2, N) + P2 (m-2, N)) If n half 1 and m = 4 m'' + 1, PO (M, n) = b (P2 (M, n-2) P2 (m-
2,n)+P4(M,n-2)・P4(m-2,n))
+P2(M,n-2)・P4(m-2,n)+P2(m
-2,n)・P4(M,n-2)P2(M,n)=h(
P4(M,n-2)・P4(m-
...(9)2,n)+P
O(M, n-2)・PO(m-2, n)) 10P4(M,
n-2)・PO(m-2,n)+P4(m-2,n)・
PO(M,n-2)P4(M,n)=A(PO(M,n
-2)・PO(m-2,n)+P2(M,n-2)・P
2(m-2,n))+PO(M,n-2)・P2(m-
2,n)+PO(m-2,n)●P2(M,n-2)n
If half N and m=4m″-1, PO(M,n)=ν(P
2(M,n+2)・P2(m-2,n)×P4(M,n
+2)・P4(m-2,n))+P2(M,n+2)・
P4(m-2,n)+P2(m-2,n)・P4(M,
n+2)P2(M,n)=ν(P4(M,n+2)●P
4 (m-29n). ．． ．． (1
0)+PO(M,n+2)●PO(m-2,n))+P
4(M,n+2)・PO(m-2,n)+P4(m-2
,n)・PO(M,n+2)P4(M,n)=A(PO
(M, n+2)・PO(m-2, n)+P2(M, n+
2)・P2(m-2,n))+PO(M,n+2)・P
2(m-2,n)+PO(m-2,n)●P2(M,n
+2).

Table 2 shows the probability distribution when φ(1,1)=0. At all odd-numbered addresses for M and n, P2 and P4 have the same value and differ from PO, but the difference from Table 1 is that as M and n become larger, the values of PO and P2 immediately approach each other. That is, at a large address of M, n, 0
, 213π, and 413π have approximately the same probability of occurrence. Also,
The effect shown in equation (5) can be obtained from the configuration of the phase sequence by
Each row is divided into the lower right and lower left, eliminating the habit of phase arrays characterized as a series of the same phase values from the upper left to the lower right within the phase sequence. FIG. 6 shows a part of the diffuser plate of the present invention using the phase sequence shown in FIG. 4. Next, another embodiment of the present invention is shown in FIGS. 7 and 8.

FIG. 7 shows a diffuser plate using the phase sequence of the present invention, in which the width L of odd-numbered rows and columns is larger than the width 1 of even-numbered rows. That is, the size of the area L×L. ．． For φ(M, n) where both m and n are even, l×1, φ(M, n) where m is odd and n is even is L×1, and φ(M, n) where m is even and n is odd. n) is 1
It is XL.

Fig. 8 shows a configuration in which the boundary of the phase region of the diffuser plate shown in Fig. 6 is covered with an opaque sampling mask. be.
As described above, the phase series and diffuser plate of the present invention shown in FIGS. 4 to 6 do not have the peculiarities of the phase series shown in FIGS. 2 and 3, and the phase series shown in FIGS. This sufficiently satisfies the four conditions.

Therefore, with the diffuser plate of the present invention, it is possible to reduce the hologram aperture to the diffraction limit, suppress coherent noise in the reproduced image, and furthermore increase the stability of the system during reproduction. Note that FIG. 6A is an explanatory top view, and the opening is an explanatory side cross-sectional view. In addition, in the diffuser plate of the present invention shown in FIG. 7, what is the size of one side of the main part of the Fourier transform pattern of the diffuser plate, which is 2λf in size? (where λ is the wavelength of the light, and f is the focal length of the L + Z-lier conversion lens). For, what is the size of the main part 4λf?

Therefore, leak L+ri The ratio between the former and the latter is Therefore, it can be seen that the former is larger.

When using the diffuser plate shown in Figure 6, the hologram aperture needs to be about 4 times the area of the main part of the Fourier transform pattern due to the relationship with the S/N of the reproduced image, but as shown in Figure 7. In the case of a diffuser plate, even if the hologram aperture matches the size of the main part of the Fourier transform pattern, the S/N is sufficient.
A good reconstructed image can be obtained. In other words, a high-density, high-quality hologram with good diffraction efficiency can be realized. Furthermore, in the embodiment of FIG. 8, since there is an opaque mask at the boundary of the phase region,
In the reproduced image, interference effects due to overlapping of images of each phase region are considerably suppressed. Also, if we consider the case where the phase regions are arranged at equal pitches on the diffuser plate in Figure 6, the main part of the Fourier transform pattern will be larger than that in the diffuser plate in Figure 6 due to the influence of the mask. A high-density, high-quality hologram with better diffraction efficiency than the diffuser plate shown in FIG. 6 can be realized. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram showing addresses of a two-dimensional phase array, FIGS. 2 and 3 are conventional phase sequence diagrams, FIGS. 4 and 5 are phase sequence diagrams of the present invention, and FIG. FIGS. 8 to 8 are explanatory diagrams of a diffusion plate according to an embodiment of the present invention.

Claims (1)

[Scope of Claims] 1. When a light beam of a specific wavelength passes through a phase plate consisting of regions of M rows and N rows (M and N are odd numbers) divided like a grid, the transmitted light flux within the same region The phase shifts of are the same, but the relative phase shifts experienced by the light beams transmitted through different regions are two-dimensional phase series {φ(m, n)}, m= corresponding to the spatial arrangement of each region of the phase plate. 1, 2, 3,...
..., M, n=1, 2, 3, . . . , N, and the phase sequence has six phase values 0, π/3, 2
/3π, π, 4/3π, 5/3π are the constituent elements, m,
A partial phase sequence composed of φ(m, n), both of which are odd numbers, includes groups of 0, 2/3π, 4/3π, or π/
Any group of 3, π, or 5/3π forms an array, and the difference between the phase value of any address in the partial phase sequence and the phase value of each of the four addresses closest to that address (top, bottom, left, and right) ga+
2/3π or -2/3π (however, positive and negative signs appear with equal probability), and each row or column is assigned so that it does not have the same phase sequence, and only one of m or n is an odd number φ (m, n) is assigned the vectorial average value of the phase values on both sides or above and below the address considered in the entire sequence, and furthermore, both m and n are even numbers φ(m, n).
n) is assigned a phase value that differs by π/3 in absolute value from the phase values on both sides of the address considered in the entire series, and the phase value of each of the six phase values as a whole is assigned to In order to form a pseudo-random diffuser plate that diffuses the luminous flux of the specific wavelength so as to be characterized by a phase sequence in which the total sum is approximately equal, both m and n are composed of odd numbers of φ (m, n). The partial phase sequence obtained by φ(1,
1), φ (3, 1), ......, φ (M, 1), φ
(M, 3), φ(M-2, 3)..., φ(1,
3) A method for forming a pseudo-random diffuser plate, characterized in that it is formed in a zigzag pattern such as φ(1, 5), φ(3, 5), etc. 2. A method for forming a pseudo-random diffuser plate according to claim 1, characterized in that the width of odd rows is larger than that of even rows, and the width of odd columns is larger than that of even columns.