JP6471031B2 - Phase filter, imaging optical system, and imaging system - Google Patents

Description

  The present invention relates to a phase filter, an imaging optical system, and an imaging system, and more specifically, a technique for reducing noise and a positional deviation of a reproduced image in an enlarged focal depth image after WFC image processing. Related to technology.

  On the pupil plane of the imaging camera optical system, by giving a phase distribution given by a cubic function to the coordinates in the pupil plane, the blur of the point image with respect to the defocus is made uniform, and the uniform blur is an image called deconvolution A technique called Wavefront Coding (hereinafter abbreviated as WFC) is proposed which is removed by processing to expand the depth of field and the depth of focus of an optical system.

  As a conventional technique related to such WFC, for example, the phase of a pupil function is modulated by a phase filter that realizes a third-order phase function in an optical system of an imaging camera, and image processing is performed on a captured image, thereby focusing the optical system. A technique for expanding the depth has been proposed (see Patent Document 1).

  Further, as a phase filter that modulates an optical transfer function (OTF), when a coordinate system orthogonal to the optical axis is set to x and y coordinates, a cubic function is represented by a series of functions expressed by a product of arbitrary powers thereof. There is also proposed a technique for expanding the depth of focus of an optical system by providing a generalized phase distribution and performing image processing on a captured image (see Patent Document 2).

  In addition, by using a phase filter that has an annular structure and each annular zone has a substantially parabolic cross-sectional shape, the spot shape in the optical axis direction is made uniform, and the depth of focus is reduced by performing uniform image processing. An expanding technique has been proposed (see Patent Document 3). Furthermore, a technique using a spiral distribution for the phase distribution has been proposed (see Patent Document 4).

US Pat. No. 5,748,371 JP 2011-120309 A JP 2014-197115 A International Publication No. 2015/004881

In Patent Documents 1 and 2, a phase filter that gives the wavefront aberration given by Equation (1) is inserted at the stop position of the imaging optical system with respect to the x-axis and y-axis defined in the pupil plane and orthogonal to each other. .

Here, α is a cubic function coefficient, and such a phase filter is called CPM (Cubic Phase Mask).

On the other hand, when a defocus wavefront aberration of the aberration coefficient β is added, the equation (1) can be transformed into the equation (2).

As shown in the equation (2), the defocus β is decomposed into a first term displacement in the pupil plane and a second term wavefront slope. The first term does not affect the intensity distribution of the image plane, and apparently does not change the wavefront shape due to the wavefront aberration of defocus, and is the basis for the blur of the point image being insensitive to defocus. However, the second term causes a position shift of the point image in proportion to the square of the amount of defocus in the focal plane, and thus becomes a problem when used in applications such as image recognition. This is the first problem to be solved by the present invention.

  On the other hand, in Patent Document 3, since an axially symmetric phase filter is used, such a problem of spot position deviation does not occur, but the same problem as in Patent Documents 1 and 2 remains for another problem described below. .

To explain another problem, a point spread function PSF (Point Spread Function), which is a point image intensity distribution, is given by Expression (3) by the Fourier transform action by the lens.
Here, F represents a two-dimensional Fourier transform operation.

Using this, a blurred image B (x, y) of an object emitting a light intensity distribution A (x, y) is given by Equation (4) by overlap integration of A and PSF.
Here, * indicates an overlap integral operation.

By performing Fourier transform on both sides, the overlap integral is converted into a product of Fourier transform, and is expressed as in Equation (5).

From this, if the PSF is uniform regardless of the defocus, an in-focus image can be obtained by the image processing calculation as in Expression (6) even if the defocus is present.

This process is called deconvolution.

Here, the Fourier transform of the PSF is called an optical transfer function OTF (Optical Transfer Function), and the optical transfer function OTF is a spatial frequency u in the x direction of the light intensity distribution emitted by the object, and a spatial frequency in the y direction. As a function of v, it is expressed as equation (7).

  Here, the point image given by the equation (3) is relatively large in the amount of aberration for obtaining the focal depth expansion effect, and accordingly, the OTF given by the equation (7) becomes a smaller value as the spatial frequency component is higher. As can be seen from the equation (6), the image processing for obtaining the reproduced image is a frequency filtering process for amplifying a high frequency component with a large amplification gain because it is divided by an OTF having a small value.

  In general, electrical noise such as thermal noise is generated in a sensor of an imaging camera, and the detected image signal is mixed uncorrelated. When the frequency filtering process with a large amplification gain according to the equation (6) is performed on the detected image in which noise is mixed, greatly amplified noise is mixed with the focused image signal. It causes deterioration of image quality. This reduced the effective depth-of-focus expansion effect when evaluated by the image performance index. That is, suppressing the increase in noise is the second problem to be solved by the present invention.

  Further, Patent Document 4 aims to uniformly blur the condensing spot in the optical axis direction by giving the phase filter a spiral wavefront shape. However, since the tilt of the phase plane in the circumferential direction at a certain radial position around the optical axis is not uniform, the tilt of the light beam is also not uniform, and the uniformity of the circumferential direction of the focused spot is broken, There is a problem that the uniformity of the spot with respect to defocusing is also deteriorated. Solving this problem is the third problem of the present invention.

  As described above, the present invention has been made to solve the above-described problems, and its purpose is to prevent the positional deviation of the reproduced image, suppress the increase in noise, and provide a spot distribution in the focal direction. It is an object to provide a phase filter, an imaging optical system, and an imaging system that realize an enlarged focal depth image having excellent uniformity.

  In order to solve the above-described problems, a typical phase filter of the present invention is a phase filter made of a transparent material and having an optical axis, and the surface of the phase filter is continuously formed around the optical axis. A light beam of a light beam incident on the optical axis in parallel with the curved surface having n inclined surfaces (where n is a natural number of 2 or more) and a step formed at the boundary between the adjacent inclined surfaces. Is deflected and refracted in the circumferential direction with respect to the optical axis through the curved surface.

  A typical imaging optical system of the present invention includes at least the above-described phase filter, an imaging lens system including a plurality of refractive surfaces, a diaphragm, and an image sensor. Further, the representative imaging system of the present invention removes the blur of the point image caused by the imaging optical system as a bright spot on the reproduced image with respect to the imaging optical system described above and the image signal output from the image sensor. An image processing circuit to be reproduced is integrally configured.

  According to the present invention, it is possible to obtain a magnified depth-of-focus image that prevents positional deviation of a reproduced image, suppresses noise increase, and has excellent uniformity of spot distribution in the focal direction. In an inspection apparatus camera, a smartphone camera, etc., it is possible to maintain reliability and widen the visual field range in the depth direction, and to reduce the initial focus adjustment accuracy. Problems, configurations, and effects other than those described above will be clarified by the following description of the embodiments.

It is a figure explaining the basic | reflecting-refractive action of the light ray by the phase filter of this invention. FIG. 2 is a projection view of light rays shown in FIG. 1 onto a virtual plane B. It is the schematic of the wavefront aberration by the phase filter of this invention in case of n = 4. It is detail drawing for demonstrating one Embodiment of the phase filter of this invention. It is a figure which shows the simulation result of PSNR by the various phase filters of Example 1 on the conditions without noise. It is a figure which shows the simulation result of PSNR by the various phase filters of Example 1 on conditions with noise. It is a figure which shows the PSNR comparison simulation result by the radius dependence of the phase distribution of the phase filter of this invention. It is a simulation result of OTF of the phase filter of the present invention. It is an OTF simulation result of CPM for comparing with the phase filter of the present invention. It is a list figure of the defocus dependence of a wavefront aberration by a phase filter of the present invention, a point image, a detection image, and a reproduction image. It is a list of the defocus dependency of wavefront aberration, point images, and detected images in a normal optical system that does not use the phase filter of the present invention. It is the position shift amount calculation result of the reproduction | regeneration image of CPM and a twist phase filter. FIG. 3 is a diagram illustrating a wavefront aberration shape of the phase filter according to the first embodiment. It is a figure which shows the phase profile of the radial direction of the phase filter of FIG. It is a figure which shows the phase profile of the circumferential direction of the phase filter of FIG. It is a figure which shows the wavefront aberration of the phase filter which concerns on Example 2 of this invention. It is a list figure of the focus shift dependence of the detection image of a normal optical system, the detection image at the time of using a phase filter in the optical system which concerns on Example 3 of this invention, and a reproduction | regeneration image. It is a figure which shows the imaging optical system and imaging system which concern on Example 4 of this invention. In Example 5 of this invention, it is a figure which shows the structure which integrated the phase filter with the lens refractive surface.

  Hereinafter, an embodiment and various examples of the present invention will be described with reference to the drawings. The following description shows specific examples of the contents of the present invention, and the present invention is not limited to these descriptions. Various modifications by those skilled in the art are within the scope of the technical idea disclosed in this specification. Changes and modifications are possible. In all the drawings for explaining the present invention, components having the same function are denoted by the same reference numerals, and repeated description thereof may be omitted.

  FIG. 1 is a diagram for explaining the basic light deflection and refraction action of the phase filter 101 according to an embodiment of the present invention. FIG. 1A is a diagram showing a light condensing action by a normal lens for comparison, in which a light beam 104 incident on the lens 102 is condensed toward a focal point 105. An outermost ray of a light beam from the virtual plane A, which is at an equal distance in the front and rear direction in the optical axis direction, from the focal point 105 to the virtual plane B through the focal point 105 is shown in the right perspective view. Since there is no aberration in the ray and the distance from the focal point 105 is equal, the ray passing through the 12 o'clock position of the virtual plane A reaches the 6 o'clock position of the virtual plane B, and so on. The hour will reach 12:00 and 9:00 will reach 3 o'clock.

  In FIG. 1B, the light beam 106 incident on the lens 103 is slightly refracted by the phase filter 101 according to the embodiment of the present invention, resulting in an optical path different from that in FIG. In the right perspective view, the light beam passing through the 12 o'clock position of the virtual plane A reaches a position near 5 o'clock in the virtual plane B instead of 6 o'clock. Similarly, at 3 o'clock, 8 o'clock, 6 o'clock at 11 o'clock, and 9 o'clock at 2 o'clock.

  Thus, the phase filter 101 refracts the light beam so as to be twisted with respect to the optical axis 10. This is hereinafter referred to as “deflection and refraction”. By deflecting and refracting the light beam 10 in this way, the focal point 105 in the normal optical system is blurred like a minimum circle of confusion 107, and becomes a condensed light beam whose beam diameter gradually increases while twisting in the optical axis direction. This makes the spot intensity distribution uniform. Hereinafter, for convenience, the light spot formed in this manner is referred to as a twisted spot, and a phase filter that generates a twisted spot is referred to as a twisted phase filter. The light rays that make up such a spot are collected in close proximity to each other without intersecting.

  FIG. 2 is a projection view of the light rays when the light rays from the virtual plane A to the virtual plane B in FIG. 1B are projected onto the virtual plane B and viewed from the virtual plane B side. In FIG. 2, the light ray starting point of the virtual plane A is shown with a small circle. Among these, the vicinity of the focal position of the light beam starting from the 12 o'clock position of the virtual plane A and reaching the 5 o'clock position of the virtual plane B is shown enlarged on the right side. The projection of this ray onto the imaginary plane B is a chord connecting 12 o'clock and 5 o'clock, and the angle formed by the diameter passing through the 12 o'clock position is defined as the twist angle γ. Assuming that the length of the string connecting 5 o'clock and 6 o'clock is w, as shown in the enlarged view on the right side of FIG. 2, the length of the perpendicular line extending from the center O to the string connecting 12 o'clock and 5 o'clock is w / It can be seen that w corresponds to the diameter of the minimum circle of confusion 107.

  The angle formed between the perpendicular and the diameter passing through 3 o'clock is equal to the twist angle γ. What is shown is the light beam at the outermost edge of the light beam, but the arrival position of the light beam at an arbitrary radial position on the focal plane is, for example, from w / 2 by the ratio of the radius to the radius of the outermost edge of the virtual plane A. It can be considered to be smaller. Here, the position of the outermost ray on the focal plane is deviated from the optical axis by w / 2. If the focal length of the lens 103 is f, the outermost ray will be w. This means that it is tilted by 2f, and the wavefront is tilted by the same amount.

If w is sufficiently smaller than the effective radius R of the lens 103, the direction of wavefront inclination at an arbitrary radial position r on the lens pupil plane is the circumferential direction of the pupil plane, and the coordinates in the pupil plane are polar coordinates (r , Φ) can be expressed as in equation (8).

Here, W (r, φ) is a wavefront aberration distribution.

Thus, the wavefront aberration that forms the torsion spot can be expressed, for example, by the equation (9).

Since this is a function that is large in a linear function with respect to the radial angle φ and quadratic in the radial direction, for example, when defined as C = 0, φ = 0 to 2π, φ = 0 is a spiral shape with a step.

Since the symmetry is poor and the angle-of-view characteristic is likely to deteriorate, the radial angle is divided into n and expressed as in equation (10).

Expression (10) can be expressed as Expression (11) by using the normalized pupil radius ρ normalized by the pupil radius R and the numerical aperture NA = R / f.

Further, at this time, the optical path difference h of the step at the outermost periphery is expressed by Expression (12).

If Expression (12) is used, Expression (11) can also be expressed as Expression (13).

  For example, when n = 4, the wavefront aberration distribution is as shown in FIG. Since the wavefront aberration is equivalent to the optical path difference generated by (N-1) d when the refractive index is N with respect to the unevenness d of the phase filter, the surface shape of the phase filter substantially reflects this shape. It becomes. FIG. 4 shows the shape of the phase filter 101 according to an embodiment of the present invention. 4A is a perspective view of the phase filter 101 according to an embodiment of the present invention as viewed obliquely from above, and FIG. 4B is a top view of the phase filter 101. FIG. As shown in FIG. 4, the phase filter 101 is made of a transparent material, and four inclined surfaces 20 for deflecting and refracting light rays are continuously formed around the optical axis 10, and the boundary between adjacent inclined surfaces 20. It has a substantially disk-like (flat plate) structure having a curved surface in which a step 30 is formed. That is, the phase filter 101 has four inclined surfaces 20 (20a to 20d) and four steps 30 (30a to 30d). The inclined surface 20 is configured to incline downward in the T direction, which is the clockwise direction of the optical axis 10 when viewed from above in FIG.

  In more detail, the phase filter 101 according to this embodiment has a 1 / n rotation around the optical axis 10 every n rotations because of the symmetry of the region between the steps 30 and 30. It has n-fold rotation identical symmetry that overlaps the original shape. That is, the phase filter 101 has a structure that is rotationally symmetric around the optical axis 10 n times (where n is a natural number of 2 or more). In the embodiment shown in FIG. 4, the inclined surfaces 20a, 20b, 20c, and 20d all have a ¼ circular shape in a plan view, and overlap each other when the phase filter 101 is rotated by ¼, and during one rotation. (4 times symmetry).

  Further, in the phase filter 101 according to the present embodiment, as shown in the above formula, the inclination angle in the circumferential direction is increased in proportion to the radius. If attention is paid to a specific radial angle, the inclination angle in the radial direction increases in the positive or negative direction in proportion to the distance from the optical axis 10. The step 30 also increases as the distance from the optical axis 10 increases. That is, the height of the step 30 is formed so as to increase as the phase filter 101 moves outward in the radial direction from the center point O where the phase filter 101 intersects the optical axis 10. Note that the phase filter 101 shown in FIG. 4 has a configuration when n = 4, but actually, for example, a configuration with n = 50 is used as described in the following various embodiments.

  Hereinafter, specific examples will be described.

  An example in which the present invention is applied to an optical system having a focal length of 50 mm, an effective diameter of 15.625 mm, an F number of 3.2, a sensor size of 15 mm square (hereinafter referred to as □), a pixel count of 1024 × 1024, and a center wavelength of 500 nm will be described. The wavelength is also calculated for 400 nm and 600 nm around the center wavelength, and an image of these average values is used as the calculation result. The sample image is a typical female face test image called Lena with 512 × 512 pixels and 256 tones, placed in the center of the 1024 × 1024 area, and the other regions are filled with 0 brightness values. .

The evaluation of the reproduced image is performed with an evaluation index called PSNR (Peak Signal to Noise Ratio) defined by the equation (14).
Here, f ′ (x, y) and f (x, y) are the luminances at the pixel (x, y) of the reproduced image and the original image, respectively. Max Value is the maximum luminance, which is 255 in this embodiment. X and Y are the number of pixels. In this embodiment, only the central Lena image is evaluated, and both are 512. This index becomes a large evaluation value with the denominator being smaller as the reproduced image is closer to the original image. The unit is dB.

  FIG. 5 shows a PSNR simulation result under the above conditions under a condition free from noise. The horizontal axis of the graph represents the defocus amount between the sensor surface and the focal point. The “normal” curve does not use a phase filter, and the PSNR value of the image formed on the sensor, “CPM (α20)” and “CPM (α60)” are α values in the equation (1), where λ is the center wavelength. Are 20λ and 60λ, respectively. However, since the CPM needs to have a rectangular aperture, a 12 mm square aperture stop is added.

  The “annular zone” is a case of an annular phase filter with a parabolic cross section groove of equal width and equal depth, and the phase depth of the parabolic cross section is 2.5λ, and the nth ring from the inside toward the outside. This is an annular phase filter in which a phase step of 5nλ is added to the band boundary.

  “Twist” is an embodiment of the torsion filter of the present invention, and is a calculated value when the number of divisions in the circumferential direction is 50 and the phase step at the division boundary at the outermost circumference is 18λ. At the focal position of Defocus = 0, the PSNR reaches 45 dB or more, but decreases as Defocus increases. If the allowable value is assumed to be 35 dB, the depth of focus under normal conditions is about 0.3 mm, CPM is about 1.0 mm at α = 60λ, about 0.6 mm at α = 20λ, and both the annular filter and the twist filter are about It is 0.8 mm, and CPM seems to have the greatest depth of focus expansion effect. However, the situation changes when there is noise.

  FIG. 6 shows the PSNR calculation result when the noise has a normal distribution noise with a standard deviation of 0.12% with respect to the maximum luminance. However, the noise of CPM is relatively larger than that of the circular opening due to the opening area ratio of the rectangular opening. In the case of α = 20λ, the peak is lowered by about 10 dB at the focus position of Defocus = 0, and the depth of focus of 35 dB or more is reduced to about 0.4 mm. In the case of α = 60λ, the peak is no longer lower than 30 dB. This is probably because the amplification gain in the deconvolution is large and the PSNR is deteriorated due to the result of amplification of random noise. Actually, the condition of α = 20λ is a condition for widening the depth of focus of 35 dB or more under this noise condition as a result of searching several α. The same applies to “annular zone” and “twist”, but the annular zone filter is slightly above the CPM of α = 20 at the peak, but the depth of focus is only about the same.

  On the other hand, the twist filter has a peak that is about 5 dB higher than the CPM, and the focal depth is about 0.7 mm, which is almost twice as large as the CPM. On the other hand, the curve displayed as “twist (equivalent to CPM)” is a twist filter when the focal depth of PSNR 35 dB or more is almost equal to CPM, and is a condition of 40 divisions and the outermost peripheral phase step 5λ. It can be seen that the PSNR at the focal position is 10 dB or more higher than the CPM at the same focal depth.

In this way, when there is noise, the torsional phase filter that generates the torsional spot of the present invention can be expected to have a remarkable depth-of-focus effect and a high S / N ratio. The calculation result of the twisted spot of 6 is not a function in which the radial phase profile is proportional to the square of the radius but a function that is proportional to the cube of the radius. That is, it was a wavefront aberration distribution given by the function of Expression (15).

  In the derivation of Expression (13), the light distribution at the focal position is intended to be arranged in a similar rotational manner to the distribution on the pupil plane. However, the spot intensity distribution does not always follow the light distribution, and wave optics. There is a great possibility that the uniformity of the intensity distribution in the optical axis direction is affected by the diffractive action. FIG. 7 shows a result of searching for a condition for maximizing the focal depth of 35 dB or more for each of the second, third, and fourth powers in the radial direction dependency. Here, in the case of the square, the level difference is 2λ, and in the case of the number of divisions of 100 and the third power, as described above, in the case of the fourth power, the level difference is 30λ and the division is 50. As described above, the depth of focus is the widest when the cube is the third power. In the case of the fourth power, the depth of focus is almost the same, and the PSNR at the focal position is about 3 dB higher than that of the third power, so it may be applicable depending on the conditions. However, since the step is as large as 30λ, it may be difficult to manufacture. In the case of the square, the focal depth is about the same as that of CPM and the annular zone, and the PSNR of the focal position is high.

  FIG. 13 shows a bird's-eye view of the calculation result of the phase distribution in the case of the cubed phase distribution of FIG. Since the axis in the vertical direction is a phase difference, it is displayed enlarged from the axis of the spatial coordinates in the plane, so that the actual unevenness of the shape of the phase filter is almost visible. FIG. 14 shows the phase distribution of the cross section in the radial direction of FIG. The value of the legend is a radial angle, which is an angular value of 11 points obtained by dividing one period between steps near the radial angle 0 into 10 parts. In the radial direction, the phase changes in a cubic function with respect to the radius at any radial angle, and the phase value similarly changes from positive to negative depending on the radial angle direction. FIG. 15 is a cross section in the circumferential direction, and shows a two-cycle region in the vicinity of a radial angle of 0 °. The legend is the normalized radius value. It can be seen that the inclination is constant at a certain radial position, and the inclination changes depending on the radial position. Further, since the step position does not change depending on the radial position, it can be seen that the step is along the radius.

  In order to confirm the effect of increasing the PSNR, FIG. 8 shows the calculation result of the twisted spot OTF. The above is an OTF image of 1024 × 1024 with a defocus of 0 obtained in the process of simulation, and one side has a spatial frequency width of 0.235 NA / λ. The bottom shows the cross-sectional profile along the x and y axes, and the horizontal axis indicates the number of pixels. The integrated value of the values in the display surface was 318.45. FIG. 9 shows a similar OTF for CPM of α = 20λ shown for comparison. The spatial frequency display area is the same as in FIG. 8, and the profile is a distribution in the direction along the x and y axes, so it appears larger than in FIG. 8, but the value is smaller in the diagonal direction as can be seen from the image. The integrated value is 281.82, which is smaller than the OTF of the twisted spot in FIG. For this reason, it is considered that the amplification gain of the deconvolution filter given by these reciprocals increases, noise is amplified, and PSNR is degraded in the CPM.

  FIG. 10 shows wavefront aberrations, point images, detected images at defocus amounts (focal shift) of −0.4 mm, −0.2 mm, 0, 0.2 mm, and 0.4 mm according to the present invention. It is a playback image. The wavefront aberration is indicated by interference fringes generated when a vertically incident non-aberration plane wave having the same wavelength is superimposed on the wavefront of monochromatic light having aberration. The point image displays the intensity distribution of 256 gradations in the 0.938 mm square range on the sensor surface with the brightness enhanced so that a weak intensity with a luminance of 1 or more can be visually recognized. The detected image shows the center image of the test image formed on the sensor surface, and the reproduced image is an image after the deconvolution image processing. The PSNR of these images with the original image corresponds to the values of the curves of “twist” in FIG. 6 and “cube” in FIG. The point image is ± 0.4 mm, and it seems that a large spot image suddenly appears in the peripheral portion, but this is due to highlighting, and the change due to defocusing is hardly seen at the original brightness level. Along with this, the blur of the detected image is less changed regardless of the defocus. After the deconvolution process, a clear image is reproduced with any defocus amount.

  Similarly, FIG. 11 shows wavefront aberrations, point images, and detected images due to defocusing when detection is performed as usual without using the phase filter in the present embodiment. Although blur may not be visible in the detected image depending on the printing state, the PSNR value corresponds to the “normal” curve value in FIGS. 6 and 7.

  FIG. 12 shows the calculation result of the positional deviation of the reproduced image in the CPM and the twisted phase filter. If there is a position shift in the reproduced image, the PSNR value becomes larger when the calculation is performed after the position shift is performed, rather than the calculation of Equation (14) at the position when the PSNR is calculated. The amount of displacement is calculated. The horizontal axis represents the defocus amount, and the vertical axis represents the positional deviation in units of pixel size. In this way, image misalignment, which has occurred greatly in CPM, can in principle be almost zero in a twisted spot. Defocus, which is slightly occurring at Defocus ± 0.6, is a luminance value from the central image to the surrounding area when PSNR is calculated only in the 512 × 512 area at the center of the 1024 × 1024 area. It is presumed that the blurring of the image is not necessarily symmetric due to the luminance distribution of the image, so that the PSNR with the original image becomes large at a slightly shifted position.

  Therefore, the positional deviation amount of this evaluation method may have such an error in a state where the blur is large. However, in practice, a reproduced image of CPM is relatively clear even with a large misalignment image, so that it can be evaluated as an essential image misregistration rather than an effect of blur asymmetry. As the shape of the characteristic curve, since the coefficient of the first order component of x and y that affects the image positional deviation is proportional to the square of the coefficient β of the focal deviation, it is shown in FIG. I think that it corresponds to the CPM curve being almost parabolic.

  When the phase filter shown in FIG. 13 is actually processed by mold forming, the shape is not rotationally symmetric, and therefore lathe processing cannot be used for processing the mold. Moreover, since it is an optical component, mirror processing is required, and polishing is not possible because there is a step, so it is necessary to apply a cutting tool at a certain cutting speed. Therefore, if the tool is entered from outside the diameter of the phase filter, it is necessary to let the tool escape at the center of the phase filter.

  Therefore, it is desirable to provide a recess at the center of the mold so that the tool is retracted from the optical surface. In order to make the mold have a concave portion, it is desirable that the phase filter has a convex portion at the center. Therefore, as shown in FIG. 16, a convex phase step (convex portion) 40 is provided at the center. Here, the step is given by a wavefront aberration amount of 10λ. Originally, in the shape given by Equation (15), the step at the boundary between adjacent fan-shaped regions becomes smaller at the center, but when the amount of wavefront aberration becomes several λ or less, interference occurs between the light incident on both sides of the step. As a result, the refraction of light rays deviates from the geometric optical refraction direction, which may reduce the effect expected in the present invention. Therefore, this influence can be eliminated by making the tip (end face) of the phase step 40 in the center part flat. As a result of simulation in such a phase filter, it was confirmed that the PSNR value slightly increased and had no adverse effect.

  Next, assuming a camera such as a smartphone or a wearable device, a simulation result under a slightly small optical system condition is shown. Here, the focal length is 4 mm, the effective diameter is 2 mm, the sensor size is 2 mm □, and the number of pixels is 1024 × 1024. Assuming that the distance between the lens and the sensor is fixed, the focus center is fixed at an object distance of 400 mm. At this time, the distance between the lens and the sensor is 4.04 mm. Under these conditions, the photographed images when the object was placed at 10 m, 1 m, 40 cm, and 20 cm were evaluated. At this time, the number of divisions in the circumferential direction of the twist filter was 50, and the outermost phase step was 8λ. As in the first embodiment, noise has a standard deviation and a maximum luminance ratio of 0.12%.

  FIG. 17 shows a simulation result image. The left column is a normal detection image without a twisted phase filter, the middle column is an image detected through a twisted phase filter, and the right column is a reproduced image obtained by deconvolution from the detected image. The numerical value in the image is the PSNR value. Although it does not reach 35 dB, it can be seen that the resolution is almost achieved for all distances.

  FIG. 18 shows an example of the imaging optical system and imaging system of the present invention. The combined lens 1301 includes a first lens 1302, a second lens 1303, an aperture 1304, a torsional phase filter 1305, a third lens 1306, and a fourth lens 1307, and light collected through them is an image in the sensor module 1308. An image is formed on the sensor 1309. Among these, the third lens 1306 is a bonded lens and also serves as an achromatic member. Further, the twisted phase filter is disposed in the vicinity of the diaphragm 1304. Furthermore, the assembled lens 1301 and the sensor module 1308 are integrated to form an imaging optical system. As the structure of the twisted phase filter 1305, any of the phase filters used in the first to third embodiments can be applied.

  The moving image output from the sensor is subjected to deconvolution calculation in real time by the image processing circuit 1310, and an image is displayed on the monitor display 1311. In the image processing circuit, noise that cannot be reduced even by using a torsional phase filter is performed by performing averaging calculation between multiple consecutive frames of time-series frame images every moment before deconvolution calculation. Repress. The reason why the averaging operation is performed before the deconvolution operation is that it is more efficient to perform averaging in a state where noise is not amplified. In addition, this embodiment is the same as the basic configuration when implemented in a size such as a smartphone or a wearable device.

  FIG. 19 shows an example in which the twisted phase filter 1405 is formed on the exit surface side of the second lens 1403, which is the optical surface closest to the stop 1404. By doing so, the number of parts can be reduced. As the structure of the twisted phase filter 1405, any of the phase filters used in the first to third embodiments can be applied.

  As described above, according to the above-described phase filter according to the embodiment of the present invention, the focal point that prevents the positional deviation of the reproduced image, suppresses the increase in noise, and is excellent in the uniformity of the spot distribution in the focal direction. A depth-enlarged image can be obtained. And by using such a phase filter, in-vehicle cameras, surveillance cameras, inspection device cameras, smartphone cameras, etc., maintain reliability and widen the visual field range in the depth direction, and relax the focus adjustment accuracy of the initial adjustment. Can do.

10 optical axis 20 inclined surface 30 step 40 phase step (convex)
101 Phase filter 102, 103 Lens 104, 106 Incident ray 105 Focus 107 Minimum circle of confusion 1301, 1401 Combination lens 1302, 1402 First lens 1303 Second lens 1304, 1404 Aperture stop 1305 Twisted phase filter 1306, 1406 Third lens 1307, 1407 Fourth lens 1308, 1408 Sensor module 1309, 1409 Image sensor 1310 Image processing circuit 1311 Monitor display 1403 Twist phase filter integrated lens 1405 Lens integral type twist phase filter

Claims (16)

A phase filter made of a transparent material and having an optical axis,
The surface of the phase filter has n inclined surfaces (where n is a natural number of 2 or more) formed continuously around the optical axis, and a step formed at the boundary between the adjacent inclined surfaces. Composed of curved surfaces,
The light beam incident parallel to the optical axis is deflected and refracted in the circumferential direction with respect to the optical axis through the curved surface ,
A phase filter in which a deflection angle in the circumferential direction of a light beam incident in parallel to the optical axis increases as a distance in a radial direction of the incident light beam from the optical axis increases . A phase filter made of a transparent material and having an optical axis,
The surface of the phase filter has n inclined surfaces (where n is a natural number of 2 or more) formed continuously around the optical axis, and a step formed at the boundary between the adjacent inclined surfaces. Composed of curved surfaces,
The light beam incident parallel to the optical axis is deflected and refracted in the circumferential direction with respect to the optical axis through the curved surface,
An absolute value of an inclination angle of each of the inclined surfaces in the circumferential direction with respect to a surface perpendicular to the optical axis increases as the distance from the optical axis increases in the radial direction . A phase filter made of a transparent material and having an optical axis,
The surface of the phase filter has n inclined surfaces (where n is a natural number of 2 or more) formed continuously around the optical axis, and a step formed at the boundary between the adjacent inclined surfaces. Composed of curved surfaces,
The light beam incident parallel to the optical axis is deflected and refracted in the circumferential direction with respect to the optical axis through the curved surface,
A phase filter , wherein an inclination angle of each inclined surface in a radial direction with respect to a surface perpendicular to the optical axis increases as a distance in the radial direction from the optical axis increases . A phase filter made of a transparent material and having an optical axis,
The surface of the phase filter has n inclined surfaces (where n is a natural number of 2 or more) formed continuously around the optical axis, and a step formed at the boundary between the adjacent inclined surfaces. Composed of curved surfaces,
The light beam incident parallel to the optical axis is deflected and refracted in the circumferential direction with respect to the optical axis through the curved surface,
The phase shape of each inclined surface along the radial direction with respect to the optical axis has a concavo-convex amount that is proportional to the cube of the distance of the incident light beam from the optical axis . 5. The phase filter according to claim 1 , wherein the curved surface has a shape that is n times rotationally symmetric about the optical axis. The angle of inclination of each inclined surface in the circumferential direction with respect to a surface perpendicular to the optical axis is constant regardless of the position in the circumferential direction at the same radial position with respect to the optical axis. The phase filter according to any one of claims 1 to 4 . 5. The phase filter according to claim 1 , wherein a height of each step is increased as a radial distance from the optical axis is increased. The curved surface is deflected and refracted so that all of the light beams incident in parallel to the optical axis are in a blurred state without twisting each other on the focal plane collected by the condenser lens. The phase filter according to any one of claims 1 to 4, wherein the phase filter is used. 5. The phase filter according to claim 1 , wherein a convex portion that protrudes along the optical axis and has a flat tip is provided in the vicinity of the optical axis. An imaging optical system comprising at least the phase filter according to any one of claims 1 to 4, an imaging lens composed of a plurality of refractive surfaces, a stop, and an image sensor. The curved surface of the phase filter, the imaging optical system according to claim 1 0, characterized in that said more than any refracting surface of the imaging lens is located at a position distance not far from the diaphragm. Wherein the curved surface of the phase filter, the imaging optical system according to claim 1 0, characterized in that it is added together on the refracting surface of the imaging lens. An imaging optical system according to claim 1 0, the image signal output from the image sensor, an image processing circuit for reproducing a bright spot on the blur is removed reproduced image of a point image by the imaging optical system An imaging system configured as an integral unit. The imaging system of claim 1 3, wherein the image signal output is a time series motion picture signal. Wherein the image processing circuit, an imaging system according to claim 1 4 wherein during the image frame of a certain time-series moving picture signal, characterized in that it comprises an averaging processing functions of at least the immediately preceding image frame . The imaging system according to claim 15 , wherein the averaging processing function is performed before processing for removing blur of the point image.