JP2014203412A - Diffraction image data creation program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a diffraction image data creation program capable of reducing unnecessary sampling, shortening a calculation time and reducing a memory usage.SOLUTION: A diffraction image data creation program according to the present invention, allows a computer to create diffraction image data by applying non-uniform Fourier transform to original image data. Though following conditions are not always required in this case, non-uniform Fourier transform using sampling map data is preferable, and further it is preferable that the sampling map data are divided into a plurality of quadrants and a distance from a boundary of quadrants up to each pixel is calculated in the non-uniform Fourier transform.

Description

  The present invention relates to a diffraction image data creation program.

  Diffraction calculation, which is one of the light propagation calculations, is used in various fields such as optical component design, three-dimensional display, microscope, and encryption technology. Generally, in the diffraction calculation, fast Fourier transform (FFT) is used for speeding up the calculation.

  However, due to FFT restrictions, it is necessary to make the sampling interval of the light propagation source and the propagation destination the same. On the other hand, the structure of a general optical component is a mixture of a slowly changing portion and a rapidly changing portion. When the diffraction calculation is performed using the above-described FFT, a lot of unnecessary sampling occurs in a slowly changing portion, and there is a problem in terms of calculation time and memory usage. This unnecessary sampling occurs as a similar problem in a three-dimensional display, a microscope, an encryption technique, and the like.

  By the way, as a well-known technique related to this diffraction calculation, for example, Non-Patent Document 1 below discloses a technique for setting different sampling intervals for the propagation source and propagation destination of Fresnel diffraction used in a wide field of optics. Non-Patent Document 2 below also discloses a technique for setting the sampling sensations of the propagation source and propagation destination of Fresnel diffraction to be different.

  In Non-Patent Document 3 below, when the distance between the propagation source and the propagation destination is a short distance, the sampling interval between the propagation source and the propagation destination of the angular spectrum method that can be calculated with higher accuracy than the Fresnel diffraction calculation is different. A technique for setting is disclosed.

Richard P. Muffoleto et al. "Shifted Fresnel diffraction for computational holography", OPTICS EXPRESS, Vol. 15, no. 9,5631- 5640 Fukai Zhang et al. "Algorithm for restructuring of digital holograms with adjustable magnesium", OPTICS LETTERS, Vol. 29, no. 14, 1668-1670 Peter Muys, “The Angular Spectrum Representation of Vector Laser Beams”, ArXiv. org, Cornell University Library

  However, although the techniques described in any of Non-Patent Documents 1 to 3 above can vary the sampling interval between the propagation source and the propagation destination, they can handle sampling at unequal intervals at each of the propagation source and the propagation destination. In the end, many unnecessary samplings occur, and the calculation time and memory usage cannot be reduced.

  Accordingly, an object of the present invention is to provide a diffraction image data creation program capable of solving the above-described problems, reducing unnecessary sampling, reducing calculation time, and reducing memory usage.

  A diffraction image data creation program according to an aspect of the present invention causes a computer to create diffraction image data using unequal interval Fourier transform for original image data.

  Moreover, although not necessarily limited from this viewpoint, it is preferable to perform unequal interval Fourier transform using sampling map data.

  Further, although not limited in this aspect, it is preferable that the sampling map data is divided into a plurality of quadrants and the distance is calculated from the boundary between the quadrants.

  As described above, according to the present invention, it is possible to provide a diffraction image data creation program capable of reducing unnecessary sampling, reducing calculation time, and reducing memory usage.

In the program which concerns on embodiment, it is an image figure in the case of dividing | segmenting an original image into several quadrants and making each the sampling distance differ. It is an image figure in the case of integrating | accumulating in order along a column or a row from the pixel of a corner position. It is an image figure in the case of dividing into a plurality of quadrants and calculating from a boundary point for each quadrant. It is a figure which shows the result in the case of integrating | accumulating in order along a column or a row from the pixel of a corner position. It is a figure which shows the result at the time of dividing | segmenting for every quadrant and calculating from the point of a boundary for every quadrant. It is an image figure at the time of dividing original image data into a some quadrant, and varying the sampling interval in each. It is an example of the result of another diffraction calculation, Comprising: It is a figure which shows intensity distribution of a propagation destination. It is an example of the result of other diffraction calculations, Comprising: It is a figure which shows the transfer distribution of a propagation destination.

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

  One of the features of the diffraction image data creation program (hereinafter referred to as “the program”) according to the present embodiment is to perform unequal interval Fourier transform processing on the original image data in a computer.

  Further, the program is not limited as long as it can be executed, but diffraction image data can be created by being stored in a recording medium of an information processing apparatus such as a so-called personal computer and executed. Specifically, for example, a program and original image data are recorded on a hard disk of a personal computer, read into a memory according to a user's execution command process, and diffracted image data is created from the original image data through a calculation process by a CPU.

  In this program, “original image data” is image data before processing, which is so-called two-dimensional image data including position information and intensity information at the position. “Diffraction image data” is a position and its data. Image data including at least one of phase information and amplitude (intensity) information at a position is described, but in the present embodiment, it is described as including phase information from the viewpoint of explanation.

As described above, this program is characterized by performing unequal interval Fourier transform processing on the original image data. Here, the “unequally spaced Fourier transform process” is a calculation process represented by the following equation.

Here, u ₁ (m ₁ ) and u ₂ (m ₂ ) are propagation wavefronts and propagation wavefronts sampled at N × N points, m ₁ , m ₂ and m _f are integer value position vectors, and z Is a propagation distance, λ is a wavelength, NUFT is an unequally spaced fast Fourier transform, FFT ^-1 is an inverse Fourier transform, and Δ is a sampling interval. The propagation wavefronts are sampled at unequal intervals, and the propagation sources are sampled at regular intervals.

The implementation of the unequal interval fast Fourier transform is not limited as much as possible, but is implemented by Greengard & Lee (L. Greengard and J. Y. Lee, “Accelerating the Nonuniform Fast Fourier Transform”, SIAM Rev. 46). 443-454 (2004) Note that for this unequal interval fast Fourier transform, Type 1 (the spatial region is unequal, the frequency region is equally spaced) and Type 2 (the spatial region is equally spaced, the frequency region) Can be selected. For example, it is convenient to use Type 1 and the discrete Fourier transform (DFT) of Type 1 can be expressed by the following equation: .

The unequal-interval fast Fourier transform is an algorithm that can calculate the above formula (2) at high speed, and includes an interpolation process by Gridding, a single FFT, and a deconvolution process that removes the effects of Gridding . u ₁ (x ₁ ) is a mapping of u ₁ (m ₁ ) in the following range, and unequal sampling can be handled within this range.

When calculating formula (1), the calculation area should be doubled horizontally and vertically (zero padding is applied to the expanded part) to avoid circular convolution, and calculation should be performed as linear convolution. Is preferred. Therefore, it is preferable to calculate N ′ in the formula (1) as N ′ = 2N. Moreover, final u ₂ (m ₂ ) can be obtained by extracting a desired N × N pixel region from u ₂ (m ₂ ) of N ′ × N ′ pixels in the following range.

  Further, in this program, it is preferable that the non-uniformly spaced fast Fourier transform is performed using sampling map data. Here, “sampling map data” refers to a set of data in which the sampling status of each pixel is recorded. The sampling map data is preferably recorded in advance on a recording medium such as a hard disk and is preferably read out during the calculation.

  The data representing the sampling status in the sampling map data is not limited as long as unequal intervals can be expressed, but is preferably data including the sampling distance of each pixel. It goes without saying that the sampling distance of each pixel is advantageous in the unequal interval Fourier transform, but it is not necessary that the sampling distance is irregular. It is preferable that the sampling distance is increased in the changing portion, and the variation is generated so that the sampling distance is shortened in the rapidly changing portion. By doing so, it is possible to reduce the calculation time and memory usage.

  In order to vary the sampling distance of each pixel, the entire image can be determined for each pixel by determining a slowly changing portion and a rapidly changing portion for each pixel. It is also preferable that the sampling distance is roughly divided into a plurality of quadrants and the sampling distance is different for each quadrant so that the sampling distance is the same within the same quadrant, and the sampling distance is concentrically formed from the center position of the sampling map data. They may be arranged differently. In this way, it is possible to suppress an increase in calculation time and memory usage due to obtaining the sampling distance.

In addition, the sampling distance in the sampling map data includes data on the distance to adjacent pixels. In the unequal-interval fast Fourier transform of this program, if there is a sampling map, x in the above formula (1) ₁ is not obtained as it is, and x ₁ needs to be generated from the sampling map. Various methods can be adopted to generate x _{1, and} the method is not limited. However, the sampling intervals from a predetermined reference position to each pixel are integrated, and the result is multiplied by 2π / N ′ to obtain x _1. It is preferable that

  This predetermined reference position can be simply accumulated in order along the column or row from the image at the corner position of the sampling map data, but when divided into a plurality of quadrants, the boundary of the quadrant More specifically, it is preferably a boundary line or a boundary point, and if it is to be deposited concentrically, it is preferably a center point. Moreover, when dividing | segmenting into several quadrants, it is preferable to make it precipitate for every quadrant. Here, FIG. 1 shows an image diagram when the original image is divided into a plurality of quadrants and the sampling distances thereof are different from each other. FIG. 1 is an image diagram when the pixels are sequentially integrated from the pixel at the corner position along the column or row. FIG. 2 shows an image diagram in the case where the calculation is performed from the boundary point for each quadrant when the image is divided into a plurality of quadrants.

  In addition, when integrating sequentially from the pixel at the corner position (upper left in FIG. 2) along the column or row, the result of the integration is to perform processing across the end (lower right) quadrant, so that a correct result is obtained. It may not be obtained (see FIG. 4). Therefore, if the image is divided into quadrants and calculated from the boundary points for each quadrant, a correct intensity distribution can be stably obtained (see FIG. 5). Therefore, it is preferable that the sampling map data is divided into a plurality of quadrants, and the distance from the quadrant boundary to each pixel is calculated in the unequal interval Fourier transform.

  In addition to the above example, an example will be described in which diffraction image data is created by performing unequal interval Fourier transform using actual image data using the angular spectrum method.

  FIG. 6 shows an image diagram when the original image data is divided into a plurality of quadrants and the sampling intervals in each of them are different. As shown in this figure, in this example, the original image data is divided into four quadrants, which are 0.6Δ (upper left in the figure), 0.8Δ (upper right in the figure), 0.5Δ (lower left in the figure), Δ ( The calculation was performed by integrating the sampling distances in the direction shown in FIG. The results are shown in FIGS. FIG. 7 shows the intensity distribution of the propagation destination, and FIG. 8 shows the transfer distribution of the propagation destination. The calculation conditions were z = 0.01 m, λ = 633 nm, and the propagation sampling interval Δ = 4 μm.

  As a result, it was confirmed that correct results could be obtained centering on the quadrant boundary points, and diffraction image data could be created very simply.

  As described above, this program has made it possible to reduce unnecessary sampling, shorten calculation time, and reduce memory usage. More specifically, since the conventional diffraction calculation performed equal-speed fast Fourier transform (FFT), it was necessary to perform sampling at equal intervals. Since the transformation (NUFT) is used, diffraction calculation can be performed at high speed even with non-uniform sampling. In addition, when this program is executed, by introducing sampling map data in which the sampling interval of each pixel from which diffraction calculation is propagated is introduced, diffraction calculation processing by NUFT can be performed easily. This sampling map data has an advantage that it can be generated from a spatial / frequency analysis technique represented by wavelet transform or the like. Furthermore, in this program, in the calculation of the sampling interval in the sampling map data, a correct diffraction calculation result can be obtained by dividing the quadrant into a plurality of quadrants and integrating each quadrant from the quadrant boundary.

  In this embodiment, the angular spectrum method is used for explanation, but the difference between the angular spectrum method and the Fresnel diffraction calculation is only the approximation of the transfer function, and this program is realized by using the Fresnel diffraction calculation. It goes without saying that it is possible.

  The present invention has industrial applicability as a diffraction image data creation program.

Claims (4)

On the computer,
A diffraction image data creation program for creating diffraction image data by using unequal interval Fourier transform on original image data.   The diffraction image data creation program according to claim 1, wherein the non-uniform Fourier transform is performed using sampling map data.   The diffraction image data creation program according to claim 2, wherein the sampling map data is divided into a plurality of quadrants, and the distance from the boundary of the quadrant to each pixel is calculated in the unequal interval Fourier transform. The diffraction image data creation program according to claim 2, wherein in the unequal interval Fourier transform, the distance from the center of the sampling map data to each pixel is calculated.