JP2015102767A - Imaging system, and phase plate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To achieve a novel imaging system for performing an increase in spherical aberration of an image forming optical system by a phase plate and image restoration by digital processing to a captured image.SOLUTION: An imaging system of this invention includes: an imaging optical system for imaging an imaging object; an imaging device for imaging the imaging object by the imaging optical system; and an image processing part for performing image processing of image data outputted from the imaging device. The imaging optical system includes: an image forming optical system for image-forming of the imaging object; and a phase plate added to the inside of the image forming optical system to increase spherical aberration of the image forming optical system to increase a focal depth. The image processing part performs restoration processing of an image obtained by increasing the spherical aberration, and imaged by the imaging optical system. The phase plate has: one surface which is flat; and the another surface as a phase modulation surface which is rotationally symmetric with respect to an optical axis of the image forming optical system and has an aspherical shape, the aspherical shape of the phase modulation surface satisfying a condition (1).

Description

  The present invention relates to an imaging system and a phase plate.

  Various “imaging systems” have been put into practical use, in which an image of an object to be imaged is imaged on a light receiving surface of an image sensor such as a CCD or CMOS by an imaging optical system.

  For example, a barcode reader that reads “a barcode added to a product”, an inspection system that reads and processes an inspection part of an “inspection object” as an imaging object, and the like.

The imaging optical system of these imaging systems is required to have a “large depth of field”.
“Deep depth of field” means that the “range of object distance” capable of capturing an appropriate image is large.

  If the range of “object distance at which a proper image can be captured” is large, for example, a good barcode image can be read even if the position of the barcode is “slightly shifted” from the proper object distance.

  Further, if an imaging optical system having a deep depth of field is used, for example, an “in-focus image of a wide inspection area” of the inspection object can be acquired.

  Recently, it has been proposed to intentionally increase spherical aberration by adding a phase plate, which is a wavefront modulation element, to an imaging optical system used in an imaging system (Patent Documents 1, 2, etc.).

  That is, the spherical aberration of the imaging optical system is intentionally increased by adding a phase plate, the imaging light beam is regularly dispersed, and a “blurred image” with large spherical aberration is formed and read.

  Then, the read image is digitally processed to restore a “good image of the imaging target”.

  Thus, by increasing the spherical aberration of the imaging optical system and restoring the image by digital processing, the “depth of field” in imaging of the imaging object can be expanded.

  An object of the present invention is to increase the spherical aberration of an imaging optical system using a phase plate, and to realize a novel imaging system that performs image restoration by digital processing on a captured image.

An imaging system of the present invention performs an image processing on an imaging optical system that captures an image of an imaging target, an imaging element that captures an image of the imaging target by the imaging optical system, and image data output from the imaging element. In the imaging system having the image processing unit, the imaging optical system is added to the imaging optical system that forms an image of the object to be imaged, and is added to the imaging optical system to increase the depth of focus. A phase plate that increases spherical aberration of an image optical system, and the image processing unit performs a restoration process on an image captured by the imaging optical system and having increased spherical aberration; Has one surface that is a plane and the other surface is a rotationally symmetric and aspherical phase modulation surface with respect to the optical axis of the imaging optical system, and the aspheric shape of the phase modulation surface is an aspherical amount. : Z, distance from rotational symmetry axis: h, normalization standard Radius: H, n order aspheric coefficients: by _{a n,} wherein:
Z = Σa _n (| h / H |) ⁿ (sum takes n = 2 to n = N for n)
In the aspheric shape represented by
Z-a ₂ (| h / H |) ²
But, from the h = 0 to the outer peripheral side monotonously changes, the outermost radius to _{h m,} aspherical amount of the position of 0.75 h _m from h = _0: and _{Z 0.75,} the h = 0 Aspheric amount: Ratio with Z ₀ is the condition: (1) 0.55 ≦ Z _0.75 / Z ₀ ≦ 0.67
It is characterized by satisfying.

  According to the present invention, it is possible to realize a novel imaging system that increases the spherical aberration of the imaging optical system by the phase plate and restores the captured image by digital processing.

It is a conceptual diagram explaining an imaging system. It is a figure which shows the lens structure of the specific example of an imaging optical system. FIG. 3 is a lateral aberration diagram with respect to a subject distance of 400 mm in the specific example of FIG. 2. FIG. 3 is a longitudinal aberration diagram with respect to a subject distance of 400 mm in the specific example of FIG. 2. It is a figure which shows the field curvature and distortion with respect to the to-be-photographed object distance: 400mm of the specific example of FIG. This is the MTF when the subject distance in the specific example of FIG. 2 is 370 mm. This is the MTF when the subject distance in the specific example of FIG. 2 is 400 mm. 2 is an MTF when the subject distance in the specific example of FIG. 2 is 430 mm. 1 is a diagram illustrating a configuration of an imaging optical system according to Example 1. FIG. FIG. 3 is a lateral aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 1. FIG. 4 is a longitudinal aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 1. These are field curvature and distortion (object distance: 400 mm) of the imaging optical system of Example 1. FIG. This is the MTF when the subject distance in Example 1 is 370 mm. This is the MTF when the subject distance in Example 1 is 400 mm. MTF when subject distance in Example 1 is 430 mm. FIG. 3 is a diagram illustrating an image processing filter (kernel filter) used for image restoration according to the first embodiment. FIG. 6 is a transverse aberration diagram (subject distance: 400 mm) when “second-order aspheric coefficient” of the phase modulation surface in Example 1 is set to 0; FIG. 5 is a longitudinal aberration diagram (subject distance: 400 mm) when “second-order aspheric coefficient” of the phase modulation surface in Example 1 is set to zero. FIG. 6 is a diagram (object distance: 400 mm) showing field curvature and distortion when the “second-order aspheric coefficient” of the phase modulation surface in Example 1 is set to zero. FIG. 6 is a diagram illustrating a configuration of an imaging optical system according to a second embodiment. FIG. 6 is a lateral aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 2. FIG. 6 is a longitudinal aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 2. These are the field curvature and distortion (object distance: 400 mm) of the imaging optical system of Example 2. This is the MTF when the subject distance in Example 2 is 370 mm. This is the MTF when the subject distance in Example 2 is 400 mm. MTF when subject distance in Example 2 is 430 mm. FIG. 10 is a diagram illustrating an image processing filter (kernel filter) used for image restoration according to the second embodiment. FIG. 6 is a diagram illustrating a configuration of an imaging optical system of Example 3. FIG. 6 is a lateral aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 3. FIG. 6 is a longitudinal aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 3. These are the field curvature and distortion (object distance: 400 mm) of the imaging optical system of Example 3. This is the MTF when the subject distance in Example 3 is 370 mm. This is the MTF when the subject distance in Example 3 is 400 mm. MTF when subject distance of Example 3 is 430 mm. FIG. 10 is a diagram illustrating an image processing filter (kernel filter) used for image restoration according to the third embodiment. It is a figure which shows the structure of the imaging optical system of the comparative example 1. 6 is a lateral aberration diagram (subject distance: 400 mm) of the imaging optical system of Comparative Example 1. FIG. 6 is a longitudinal aberration diagram (subject distance: 400 mm) of the imaging optical system of Comparative Example 1. FIG. These are the field curvature and distortion (subject distance: 400 mm) of the imaging optical system of Comparative Example 1. This is the MTF when the subject distance in Comparative Example 1 is 370 mm. This is the MTF when the subject distance in Comparative Example 1 is 400 mm. This is the MTF when the subject distance in Comparative Example 1 is 430 mm. 6 is a diagram illustrating an image processing filter (kernel filter) used for image restoration in Comparative Example 1. FIG. It is a figure which shows the structure of the imaging optical system of the comparative example 2. 10 is a lateral aberration diagram (subject distance: 400 mm) of the imaging optical system of Comparative Example 2. FIG. 10 is a longitudinal aberration diagram (subject distance: 400 mm) of the imaging optical system of Comparative Example 2. FIG. These are field curvature and distortion (subject distance: 400 mm) of the imaging optical system of Comparative Example 2. This is the MTF when the subject distance in Comparative Example 2 is 370 mm. This is the MTF when the subject distance in Comparative Example 2 is 400 mm. MTF when subject distance of Comparative Example 2 is 430 mm. 10 is a diagram illustrating an image processing filter (kernel filter) used for image restoration in Comparative Example 2. FIG. It is a figure which shows the shape of a phase modulation surface about the Examples 1-3 and Comparative Examples 1 and 2 when a secondary aspherical coefficient is set to 0. FIG. 53 is a partially enlarged view of FIG. 52. Is a diagram showing the relationship between amount of sag ratio and the MSE for 0.75 h _m. It is a diagram showing the relationship between amount of sag ratio and the MSE for 0.5h _m. FIG. 6 is a diagram illustrating a configuration of an imaging optical system according to a fourth embodiment. FIG. 6 is a lateral aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 4. FIG. 6 is a longitudinal aberration diagram (subject distance: 400 mm) of the imaging optical system according to Example 4. These are field curvature and distortion (object distance: 400 mm) of the imaging optical system of Example 4. This is the MTF when the subject distance in Example 4 is 370 mm. This is the MTF when the object distance in Example 4 is 400 mm. MTF when subject distance in Example 4 is 430 mm. 42 is a diagram illustrating an image processing filter (kernel filter) used for image restoration in Example 43. FIG.

Hereinafter, embodiments will be described.
FIG. 1 is a conceptual diagram illustrating an imaging system.

  In FIG. 1, reference numeral 201 indicates an “imaging target”, reference numeral 202 indicates an “imaging optical system”, reference numeral 203 indicates a “phase plate”, and reference numeral 204 indicates an “aperture stop of the imaging optical system”.

  Reference numeral 205 denotes an “imaging device”, and reference numeral 206 denotes an “image processing unit”.

  Hereinafter, the imaging target 201 is also referred to as “subject 201”. The imaging optical system 202 having the aperture stop 204 and the phase plate 203 constitute an “imaging optical system”.

  The subject 201 may be various ones such as the “inspection object” described above, but “articles such as products with barcodes or two-dimensional codes” are assumed below for the sake of concreteness of explanation.

  Therefore, the barcode or two-dimensional code attached to the article is an “image to be imaged”. Hereinafter, this is referred to as “image to be captured”.

  The imaging optical system 202 includes a plurality of lenses and an aperture stop. The imaging optical system 202 itself has a well corrected aberration.

  In this example, the phase plate 203 is disposed on the object side of the aperture stop 204 in the vicinity of the aperture stop, and constitutes an “imaging optical system” together with the imaging optical system 202.

  The phase plate 203 is for generating “aberration for expanding the depth of field”, and regularly diffuses the imaging light flux.

  In other words, the point spread function (PSF) on the light receiving surface of the image sensor 205 is diffused so as to “over two pixels or more”.

  An image of the imaging target image of the subject 201 is formed on the light receiving surface of the imaging element 205 by the “imaging optical system”. The image to be formed has an increased aberration by the phase plate 203.

  The increased aberration is specifically “spherical aberration”.

  As described above, the imaging optical system 202 is well corrected for “aberration by itself”, and can be used as a normal optical system without the phase plate 203.

  In the embodiment being described, the phase plate 203 is detachable from the imaging optical system 202.

  As the image sensor 205, a general solid-state image sensor such as a CCD or a CMOS sensor can be used.

  The image sensor 205 outputs “image data” of the captured image, and the output image data is input to the image processing unit 206.

  The image processing unit 206 performs digital processing for restoring “PSF diffused by inserting the phase plate 203” (hereinafter referred to as “restoration processing”).

  For example, a computer can be used as the image processing unit 206. In this case, the restoration process can be executed as a program process by software.

  Alternatively, the image processing unit 206 may be configured as hardware using an FPGA in which a processing program is written.

The image subjected to the restoration process by the image processing unit 206 is “image output”.
The image output is displayed on a display (not shown), printed, or processed by a computer or the like.

Hereinafter, a description will be given according to a specific example.
FIG. 2 shows a lens configuration of the imaging optical system 202. Since this figure shows an “imaging optical system”, the phase plate 203 is not attached.

  As shown in FIG. 2, the imaging optical system is composed of “six lenses”. The left side of the figure is the object side, and the right side is the image side.

  The imaging optical system includes lenses L1, L2, and L3, an aperture stop S, and lenses L4, L5, and L6 in order from the object side to the image side.

  The aperture stop S corresponds to that indicated by reference numeral 204 in FIG.

  The symbol IS in FIG. 1 indicates the image plane.

  Table 1 shows data of the imaging optical system shown in FIG.

  In Table 1, “Type” means a lens form, and “STANDARD” means that the lens is a “normal spherical lens”.

  “Curvature” means “curvature”, “Thickness” means “surface spacing”, and “Glass” means “glass”. “Semi-Diameter” means “effective radius”.

In the above notation, for example, “8.21E-02” means “8.21 × 10 ⁻² ”.
The leftmost column in Table 1 is “surface number” counted from the object side.

  In the following, these notations are the same.

  The imaging optical system whose data is shown in Table 1 includes six spherical lenses L1 to L6 and an aperture stop S. Hereinafter, the imaging optical system having the data shown in Table 1 is referred to as a “specific example”.

  The seventh surface is the surface of the aperture stop S as counted from the object side.

  In a specific example of the imaging optical system, FIG. 3 shows a lateral aberration diagram and FIG. 4 shows a longitudinal aberration diagram (spherical aberration) when the object distance is “from the lens L1 to 400 mm”.

  FIG. 5 shows a diagram of “field curvature (left diagram) and distortion (right diagram)” at this time. As is apparent from these figures, each aberration is sufficiently suppressed, and the imaging performance is good.

In a specific example, FIGS. 6, 7, and 8 show MTFs when the subject distance is “from the lens L <b> 1 370 mm, 400 mm, 430 mm”.
6 to 8, the vertical axis represents the MTF, and the horizontal axis represents the spatial frequency.
“S” represents sagittal and “T” represents tangential. The numerical value to the right of “S, T” is “image height”.

  The specific example in the description is designed with a subject distance of 400 mm, and therefore, the focus is achieved when the subject distance is 400 mm.

  The MTF in this in-focus state is as shown in FIG. 7, and is 0.5 or more even at a spatial frequency of 60 Cycle / mm.

  However, when the subject distance is 370 mm (FIG. 6) or 430 mm (FIG. 8), the MTF is 0 at “around 50 cycle / mm”, and the formed subject image is blurred.

  As for the aberration diagrams and the MTF diagrams, the aberration diagrams and the MTF diagrams all show light having wavelengths of 486 nm, 588 nm, and 656 nm.

  However, the “imaging optical system” used in the examples and comparative examples described below is the same, and this imaging optical system is well corrected for chromatic aberration.

  Further, since the wavelength of light is not particularly a problem in the present invention, in the following description, it is sufficient to refer to the entire aberration / MTF shown in each aberration diagram / MTF diagram.

"Description of Examples and Comparative Examples"
Hereinafter, examples and comparative examples for the imaging optical system will be described.
As described above, the imaging optical system is “an imaging optical system with a phase plate attached”.

  In all of the examples and comparative examples described below, the imaging optical system is the same as that of the specific example described above, and has the data shown in Table 1.

  In each of the examples and comparative examples, the “different part” is only the part of the phase plate mounted on the imaging optical system (specific example).

  Accordingly, in each of the drawings showing the lens configuration in these figures, the symbols L1 to L6 and S in FIG. 2 are commonly used for the lens and the aperture stop.

  Further, in these drawings, the common code “PL” is used for the phase plate.

"Example 1"
FIG. 9 shows an optical configuration of the first embodiment according to FIG.

  In the imaging optical system of Example 1, the phase plate PL is disposed close to the aperture stop S between the lens L3 and the aperture stop S of the imaging optical system of the “specific example”.

  The data of Example 1 is shown in Table 2.

  The surfaces of surface numbers 7 and 8 in Table 2 are “object-side and image-side surfaces of the phase plate PL”, and the surface of surface number 8 that is the image-side surface is “ASPHERE”, that is, “aspherical surface”.

  The surface with surface number 7 is a flat surface.

That is, the image side surface of the phase plate PL is an “aspherical phase modulation surface”.
As in this example, it is desirable to arrange the phase modulation surface as close to the aperture stop as possible.

  When the phase modulation surface is separated from the aperture stop, the phase modulation surface is likely to be enlarged in order to make the “phase modulation action” function for the entire light beam passing through the aperture stop.

  In this specification, “aspheric shape representing a phase modulation surface” is expressed by the following equation.

That is, the aspherical amount: Z, the distance from the axis of rotational symmetry: h, normalized reference circle radius: H, n order aspheric coefficients: by a _n, expressed by the following equation.

Z = Σa _n (| h / H |) ⁿ
In this aspherical formula, the sum of the right side is the sum from n = 2 to n = N. N is appropriately set according to design conditions. The rotational symmetry axis coincides with the optical axis of the imaging optical system.

  Table 3 shows aspherical data of the phase modulation surface in the phase plate used in the imaging optical system of Example 1.

  The phase modulation surface of Example 1 is a 10th-order aspheric surface, and N = 10.

  In the imaging system of the present invention, one surface of the “phase plate” used in the imaging optical system is a flat surface, as is clear from the case of Example 1 being described.

  The other surface is a rotationally symmetric and aspherical phase modulation surface with respect to the optical axis of the imaging optical system, and monotonously changes from h = 0 toward the outer peripheral side (that is, monotonically increases or decreases monotonously).

The phase modulation surface used in the imaging system of the present invention also has the following conditions:
(1) 0.55 ≦ Z _0.75 /Z≦0.67
Satisfied.

In the formula _{(1), Z 0.75} is the outermost radius (effective diameter radius): "aspherical amount of the position of 0.75h from h = 0 _{m" h m} to, _{Z 0} is "h = 0 Is the aspherical amount at.

  FIG. 10 shows the lateral aberration of the imaging optical system of Example 1 (a specific example of the imaging optical system with a phase plate added), FIG. 11 shows the longitudinal aberration, and FIG. 12 shows the distortion and distortion, respectively.

  As can be seen from comparison between FIGS. 11 and 4 showing longitudinal aberration (spherical aberration), the spherical aberration of Example 1 is larger than that of the specific example as compared with the specific example without the phase plate.

Such an “increase in spherical aberration” is an action of the phase plate PL, and the spherical aberration is intentionally given by the addition of the phase plate PL.
On the other hand, when comparing the distortion in the right diagram of FIG. 12 with FIG. 5 relating to the specific example, the “variation in distortion due to the presence or absence of the phase plate” is 0.1% or less.
In other words, the phase plate PL of Example 1 “increases only the spherical aberration without substantially affecting the distortion”.
Further, when the longitudinal aberration diagram of FIG. 11 and the curvature of field of the left diagram of FIG. 12 are viewed, “paraxial image plane shift” occurs in the first embodiment.
Although this will be described later, the influence of the secondary aspherical coefficient of the phase plate is large.

FIGS. 13 to 15 show the MTFs when the subject distances of Example 1 are 370 mm, 400 mm, and 430 mm, respectively.
In the “specific example” having no phase plate, the MTFs of the subject distances: 370 mm and 430 mm are 0 at 60 Cycle / mm or less.

  On the other hand, in Example 1, the MTF remains “not 0 even at 60 Cycle / mm” even when the subject distance is 370 mm and 430 mm.

  Thus, “the MTF does not become 0 even in a high spatial frequency region” is an effect of using the phase plate.

On the other hand, the MTF at the object distance: 400 mm is “low overall”.
That is, although the “MTF is lowered as a whole” by the insertion of the phase plate, the MTF value does not become 0 in a wide range, and “the depth of field is expanded”.

  In the present invention, restoration processing by the image processing unit is performed on image data output from the light receiving element (image data of a captured image in which spherical aberration is increased by the phase plate).

  This restoration process is a digital process, which will be described below.

  The restoration process is a process of restoring “the MTF that has been lowered overall” by the action of the phase plate, and can be performed by various known methods.

  For example, as the image restoration processing, “inverse transformation processing using a general inverse filter or Wiener filter”, “maximum entropy method”, or the like can be used.

Hereinafter, a restoration process based on the Wiener filter will be exemplified.
The Wiener filter is a general image processing filter and has been widely known.

  That is, assuming that the spatial frequency is “ω” and the image processing filter is “R (ω)”, the following equation (A) is defined.

(A) R (ω) = H (ω) ^* / [| H (ω) | ² + {S (ω) ² / W (ω) ² }]
In Expression (A), “H (ω)” is the OTF of the imaging optical system, “S (ω) ² ” is the power spectrum of the imaging target, and “W (ω) ² ” is the power spectrum of noise specific to the imaging device. It is.

“H (ω) ^* ” is a complex conjugate amount of OTF: H (ω).

  In principle, the Wiener filter may be used as an image processing filter, but the Wiener filter is a “filter having a spatial frequency as a variable”, and the calculation is likely to be complicated.

  That is, in this case, it is necessary to convert the image data to be subjected to calculation by the filter into data having a variable spatial frequency: ω by Fourier transform.

  Therefore, in the following example, image processing using a “kernel filter obtained by Fourier transforming a Wiener filter” as an image processing filter will be described.

  The kernel filter is easy to calculate because it uses real space coordinates as variables.

  Of course, processing using a kernel filter obtained by Fourier transforming “image processing filter: R (ω)” is “processing based on image processing filter: R (ω)”.

  Therefore, hereinafter, the “kernel filter” is also referred to as an image processing filter.

  For the sake of concreteness of explanation, the “pixel pitch (arrangement pitch of individual minute light receiving elements)” in the image pickup element on which the subject image is formed by the image pickup optical system is set to 8.0 μm.

  FIG. 16 shows a “kernel filter” for the first embodiment created based on the image processing filter: R (ω) created by the above formula (A).

  The size of the kernel filter is “19 × 19”.

  A convolution operation (digital operation) between the kernel filter and “acquired image data” is performed. This calculation is a restoration process.

By the way, when a phase plate is inserted in the vicinity of the aperture stop, “aspherical second-order term forming a phase modulation surface (= a ₂ (| h / H |) ² )” is defocused (image plane shift). ) Only, and not other aberrations such as spherical aberration.
This can be understood from the fact that the ^second term “2ρ ² −1” of the pupil function expressed by the “standard Zernike polynomial” has the property of focus shift.

That is, it is considered that the phase plate is arranged on the pupil plane and gives a phase difference having the same shape as the phase modulation plane to the pupil function in wave optics.
That is, it can be said that the second-order aspheric term of the phase plate is equivalent to the “second-order term of the pupil function” and provides a focus shift effect.
Incidentally, aberration diagrams when the “second-order aspheric coefficient” of the phase modulation surface in Example 1 is 0 are shown in FIGS.

In particular, as can be seen by comparing the longitudinal aberration of FIG. 18 and the curvature of field of the left figure of FIG. 19 with those of the specific example, these aberrations are “the aberration curve shape remains the same as the specific example, Only the axial image plane is shifted to the left.
That is, the secondary aspheric coefficient can be used to “shift the paraxial image plane”.
On the other hand, since the spherical aberration is not affected at all, there is no influence on the MTF characteristic and the “depth-of-field expansion effect”.

  In other words, in the aspherical surface forming the phase modulation surface, “the second-order aspherical term may have any value, and the shape represented by the third or higher order” is important.

"Example 2"
FIG. 20 shows an optical configuration of the second embodiment according to FIG.

  In the imaging optical system of Example 2, the phase plate PL is arranged close to the aperture stop S between the lens L3 and the aperture stop S of the imaging optical system of the “specific example”.

  The data of Example 2 is shown in Table 4.

The surfaces of surface numbers 7 and 8 in Table 4 are “object-side and image-side surfaces of the phase plate PL”.
The surface of surface number 8 that is the image side surface is an aspherical surface.

  The surface with surface number 7 is a flat surface.

That is, the image side surface of the phase plate PL is an “aspherical phase modulation surface”.
Table 5 shows aspherical data of the phase modulation surface in the phase plate used in the imaging optical system of Example 2.

  The phase modulation surface of Example 2 is a 10th-order aspheric surface, and N = 10.

  FIG. 21 shows the lateral aberration, FIG. 22 shows the longitudinal aberration, and FIG. 23 shows the field curvature and distortion of the imaging optical system of Example 2.

  MTFs of the imaging optical system of Example 2 are shown in FIGS. The subject distances corresponding to FIGS. 24, 25, and 26 are 370 mm, 400 mm, and 430 mm, respectively.

  FIG. 27 shows a kernel filter that is an image processing filter when the imaging optical system of the second embodiment is used.

"Example 3"
FIG. 28 shows the optical configuration of Example 3 according to FIG.

  In the imaging optical system of Example 3, the phase plate PL is disposed in the vicinity of the aperture stop S between the lens L3 and the aperture stop S of the imaging optical system of the “specific example”.

  The data of Example 3 is shown in Table 6.

The surfaces of surface numbers 7 and 8 in Table 6 are “object-side and image-side surfaces of the phase plate PL”,
The surface of surface number 8 that is the image side surface is an aspherical surface.

  The surface with surface number 7 is a flat surface.

That is, the image side surface of the phase plate PL is an “aspherical phase modulation surface”.
Table 7 shows aspherical data of the phase modulation surface in the phase plate used in the imaging optical system of Example 3.

  The phase modulation surface of Example 3 is a 10th-order aspheric surface, and N = 10.

  FIG. 29 shows lateral aberrations, FIG. 30 shows longitudinal aberrations, and FIG. 31 shows field curvature and distortion of the imaging optical system of Example 3.

  Moreover, the MTF of the imaging optical system of Example 3 is shown in FIGS. The subject distances corresponding to FIGS. 32, 33, and 34 are 370 mm, 400 mm, and 430 mm, respectively.

  FIG. 35 shows a kernel filter that is an image processing filter when the imaging optical system according to the third embodiment is used.

Comparing the “longitudinal aberration diagrams (spherical aberration)” of Examples 1 to 3, the longitudinal aberration diagrams of Example 1 and Example 2 “having an inflection point at a position where the pupil height is about 1/2” It is common.
The “longitudinal aberration diagram” of Example 3 is slightly different from those of Examples 1 and 2, and is “linear aberration with a certain inclination”.

In the “imaging optical system designed on the premise of image processing” as in the present invention, it is impossible to simply estimate whether the performance is good or bad from MTF and aberration.
This is because an “image restored by image processing” may be good even if the MTF of the imaging optical system is low.

  Here, two comparative examples are given.

  In these two comparative examples, a phase plate having a phase modulation surface shape different from those of the first to third embodiments is added to the imaging optical system described above as the “specific example”.

  Therefore, the difference between Comparative Examples 1 and 2 described below and Examples 1 to 3 is only “difference in phase plate”.

  The phase plate PL used in the first to third embodiments is a rotation target with respect to the optical axis of the imaging optical system.

  As a phase plate having such a “phase modulation surface that is rotationally symmetric with respect to the optical axis of the imaging optical system”, a “phase plate that gives third-order spherical aberration” has been known.

This phase plate has an aspheric shape of the phase modulation surface: Z (h)
Z = a ₂ h ² −a ₄ h ⁴
It is represented by

Here, since the “second order term: a ₂ h ² ” does not affect the optical performance, it is substantially a phase plate composed of only the “fourth order term: −a ₄ h ⁴ ”. .
Comparative Example 1 and Comparative Example 2 use the phase plane shape represented by this equation.

"Comparative Example 1"
FIG. 36 shows the optical configuration of Comparative Example 1 according to FIG.

  In the imaging optical system of Comparative Example 1, the phase plate PL is disposed close to the aperture stop S between the lens L3 and the aperture stop S of the imaging optical system of the “specific example”.

  The data of Comparative Example 1 is shown in Table 8.

  In Table 8, the surfaces with surface numbers 7 and 8 are “object-side and image-side surfaces of the phase plate”, and the surface with surface number 8 that is the image-side surface is an aspherical surface.

  The surface with surface number 7 is a flat surface.

That is, the image side surface of the phase plate PL is an “aspherical phase modulation surface”.
Table 9 shows aspherical data of the phase modulation surface in the phase plate used in the imaging optical system of Comparative Example 1.

As described above, the second order term is appropriate and does not affect the optical performance. 3 order aspherical coefficients: _{a 3} subsequent _{coefficients:} a 5 _{~a 10} are fourth order coefficient: a all but _{a 4} "0".

  37 shows “lateral aberration” of Comparative Example 1, FIG. 38 shows “longitudinal aberration”, and FIG. 39 shows “field curvature and distortion”.

  In addition, FIGS. 40 to 42 show MTFs when the subject optical distances of the imaging optical system of Comparative Example 1 are 370 mm, 400 mm, and 430 mm, respectively.

  FIG. 43 shows a kernel filter used for restoration processing for image data picked up by the image pickup optical system of Comparative Example 1.

"Comparative Example 2"
FIG. 44 shows the optical configuration of Comparative Example 2 according to FIG.

  In the imaging optical system of Comparative Example 2, the phase plate PL is disposed close to the aperture stop S between the lens L3 and the aperture stop S of the imaging optical system of the “specific example”.

  The data of Comparative Example 2 is shown in Table 10.

  Table 11 shows the aspherical data of the phase modulation surface of the phase plate used in the imaging optical system of Comparative Example 2, following Table 9.

As described above, the second order term is appropriate and does not affect the optical performance. 4-order aspherical coefficients: coefficient of a ₄ or later are all "0".

  45 shows “lateral aberration” of Comparative Example 2, FIG. 46 shows “longitudinal aberration”, and FIG. 47 shows “field curvature and distortion”.

  In addition, FIGS. 48 to 50 show the MTFs when the subject optical distances of the imaging optical system of Comparative Example 2 are 370 mm, 400 mm, and 430 mm, respectively.

  Further, FIG. 51 shows a kernel filter used for restoration processing for image data captured by the imaging optical system of Comparative Example 2.

  Above, the specific example of the imaging system was given as Examples 1-3 and Comparative Examples 1 and 2.

  In the following, these evaluations will be described.

  As described above, in the “imaging optical system designed on the assumption of image processing”, “an image restored by image processing” may be good even if the MTF of the imaging optical system is low.

Therefore, it is not appropriate to simply evaluate whether the performance is good or bad based on MTF and aberration.
The quality of the imaging system is considered to be determined by how close the “restored image” is to the “ideal image”.

  This evaluation is performed by “MSE” and “filter gain: GF” described below.

  “MSE” is related to [mse] defined as the following formula: (B).

(B) mse
= ∫ {| 1-R (ω) H (ω) | ² · | S (ω) | ² + | R (ω) | ² · | W (ω) | ² } dω
In Expression (B), “R (ω)” is an image processing filter, and “H (ω)” is an OTF of the imaging optical system.

“S (ω) ² ” is the power spectrum of the object to be imaged, and “W (ω) ² ” is the power spectrum of noise specific to the image sensor.

  The filter gain: FG is “image processing filter: average value for all frequencies of R (ω)”.

  “Mse” is basically defined as follows.

mse = ∫ | S (ω) −R (ω) · X (ω) | ² dω
That is, mse corresponds to the mean square error amount of “ideal image: S (ω)” and “real image: product of X (ω) and image processing filter: R (ω)”.

  Expression (B) is an expression obtained by eliminating X (ω) from the above expression.

  As the value of “mse” decreases, it can be determined that the “image restored by image processing” approaches the ideal image and a good image can be obtained.

  Therefore, the average value: MSE of the maximum, intermediate, and minimum values of the subject distance within the depth of field of the above “mse” is used as an evaluation parameter.

  Table 12 shows MSE and FG in Examples 1 to 3 and Comparative Examples 1 and 2.

  In the following description, the maximum value of the subject within the depth of field is 430 mm, the intermediate value is 400 mm, and the minimum value is 370 mm.

  In obtaining the values in Table 12, H (ω), S (ω), and W (ω) are all the same as those used when creating the Wiener filter defined by the formula (A). Yes.

As in the case of creating the Wiener filter, S (ω) and W (ω) are set to appropriate values.
As a basis for calculating the values in Table 12, it is assumed that “S (ω) ² is about 0.003”, “W (ω) ² is about 0.00001”, and “constant for all frequencies”. Went.

  As shown in Table 12, “MSE” at subject distances of 370 mm, 400 mm, and 430 mm is 0.101, 0.115, and 0.095 in Examples 1 to 3, respectively.

  On the other hand, in Comparative Examples 1 and 2, “MSE” at subject distances of 370 mm, 400 mm, and 430 mm is 0.178 and 0.157, respectively.

Comparing “MSE” of Comparative Examples 1 and 2 and Examples 1 to 3, the example is “lower overall” compared to the comparative example, and “an image closer to the ideal image” can be obtained. is made of.
When the filter gain: FG is compared, the value of the example is lower than that of the comparative example.
Filter gain: FG is an index of “how much the MTF is lifted” by the image processing filter, and the lower the value of FG, the smaller the amount of lifting of the MTF.
When amplifying the MTF by image processing, a “sensor-specific noise component” is also amplified. Therefore, it is preferable that the value of FG is small.

  In Examples 1-3, it turns out that the increase in noise can be suppressed compared with a prior art example.

  As described above, the smaller the MSE value is, the closer the image to be restored is to “close to the ideal image”, and the smaller the FG value is, the more the amplification of the “sensor-specific noise component” can be suppressed.

The value of MSE is subject to the following conditions:
(4) MSE <0.13
Is preferably satisfied.

Moreover, the value of FG is the following conditions:
(5) FG <3.8
Is preferably satisfied.

  When the upper limit of the condition (4) is exceeded, it is difficult to restore the image satisfactorily, and when the upper limit of the condition (5) is exceeded, the amplification of the noise component cannot be sufficiently suppressed.

  By satisfying the conditions (4) and (5), an “image closer to an ideal image and less noise” can be obtained as a restored image.

  Looking at the longitudinal aberration diagrams of Example 1 and Example 2 (FIGS. 11 and 22), these are common in the following points.

  That is, the longitudinal aberration curve gradually increases in inclination from the center of the pupil toward the outer periphery, and changes to “inflection point while passing through the image plane” at about ½ of the outermost periphery of the pupil.

  Furthermore, “the inclination is substantially 0” near the outermost periphery of the pupil.

  Further, the longitudinal aberration (FIG. 28) of Example 3 is “linear aberration with constant inclination”.

  On the other hand, looking at the longitudinal aberration diagrams of Comparative Examples 1 and 2 (FIGS. 33 and 38), these longitudinal aberration curves are all “monotonic curves having no inflection points”.

  That is, the “shape” of the longitudinal aberration in Examples 1 and 2 and Example 3 is a shape that can be clearly distinguished from the longitudinal aberration in Comparative Examples 1 and 2, and this is “the shape of the phase modulation surface of the phase plate to be used”. Corresponds to “difference”.

The shapes of the phase modulation surfaces of Examples 1 to 3 and Comparative Examples 1 and 2 are shown in FIG.
In FIG. 52, “Real 1, Real 2, Real 3” indicates “Example 1, Example 2, Example 3”.

  “Ratio 1, Ratio 2” indicates “Comparative Example 1, Comparative Example 2”.

  “Conventional example 1, conventional example 2” on the right side of the figure means “comparative example 1, comparative example 2”.

This figure shows a cross-sectional shape by a plane passing through the center of the phase modulation surface and parallel to the optical axis of the imaging optical system, the vertical axis is the “sag amount”, and the horizontal axis is the radial direction.
However, as described above, since the second-order aspheric term does not affect the performance, “profile when the second-order aspheric coefficient is 0: (Z−a ₂ (| h / H |) ² )” is drawn. ing.
Further, in order to make the difference in shape easy to understand, the maximum value of the sag amount (height) is all normalized to 1, and the maximum radius is normalized to 1 in the radial direction.

The “difference in the sag amount of the shape of the phase modulation surface” affects the absolute value of the aberration amount.
For example, when the amount of sag is increased, the absolute value of aberration is increased without changing the curve shape (profile) of longitudinal aberration. Changing the sag amount does not change the shape of the aberration.

  Therefore, the “characteristic aberration profile” of the first to third embodiments described above is unchanged even when the sag amount of the phase modulation surface is changed.

  That is, it is not the amount of sag but the shape that characterizes the phase modulation surface of the phase plate of the present invention.

FIG. 53 is a partially enlarged view of FIG.
In FIG. 53, “Real 1, Real 2, Real 3” indicates “Example 1, Example 2, Example 3.”

  “Ratio 1, Ratio 2” indicates “Comparative Example 1, Comparative Example 2”.

  “Conventional example 1, conventional example 2” on the right side of the figure means “comparative example 1, comparative example 2”.

Comparing the cross-sectional shapes of the phase modulation surfaces, the sag amount of Examples 1 to 3 passes around the middle of Comparative Examples 1 and 2 around a normalized radius of 0.5 to 0.9.
This is a characteristic shape of the phase modulation surface of the phase plate of the present invention.
In the column of "relative sag" in Table 12, the "effective radius" is the radius of the outermost periphery of the phase modulation plane: a h _m, 52, FIG. 53, it is normalized to 1.

It is shown in Table 12, "effective radius × 0.75", "effective radius × 0.5", _{respectively,} is 0.75 h m, 0.5h _m.

  The sag amount is a value obtained by “normalizing the maximum value of the sag amount (height) to all 1”.

That is, the aspherical amount of the position of 0.75 h _m from h = _0: and _{Z 0.75,} the aspherical amount at h = 0: the ratio of the _{Z 0: Z 0.75 / Z 0} , of 0.5h _m The ratio of the aspheric amount of the position: Z _0.5 and the aspheric amount: Z ₀ is Z _0.5 / Z ₀ .

  54 and 55 show the relationship between the “sag amount ratio” and the MSE in Examples 1 to 3 and Comparative Examples 1 and 2. FIG.

  54 and 55, “Real 1, Real 2, Real 3” indicates “Example 1, Example 2, Example 3”, and “Ratio 1, Ratio 2” indicates “Comparative Example 1, Comparative Example 2”. Is shown.

The sag amount ratio on the horizontal axis in FIG. 54 represents “Z _0.75 / Z ₀ ”, and the sag amount ratio on the horizontal axis in FIG. 55 represents “Z _0.5 / Z ₀ ”.

In Examples 1 to 3, Z _0.75 / Z ₀ falls within the “range of 0.55 to 0.67”, and Z _0.5 / Z ₀ falls within the “range of 0.85 to 0.95”. It is settled.

As shown in FIG. 54, in Examples 1 to 3 as described above, the “sag amount ratio: Z _0.75 / Z ₀ ” satisfies the condition (1), thereby realizing “MSE smaller than 0.13”. Yes.

As shown in FIG. 55, in Examples 1 to 3 as described above, “MSE smaller than 0.13” is realized when the sag amount ratio: Z _0.5 / Z ₀ satisfies the condition (2). Yes.

  In the first to third embodiments shown above, the shape of the phase modulation surface is “a surface shape that becomes a convex surface when the secondary aspherical coefficient is 0”.

  However, the present invention is not limited to this, and the shape of the phase modulation surface may be a concave surface as long as the relative sag amount falls within the above value.

As an example, an example (imaging optical system) obtained by inverting the sign of the “third-order to tenth-order aspheric coefficient” of the aspheric shape of the phase modulation surface in the first embodiment is shown as a fourth embodiment.
FIG. 56 shows an optical configuration of the fourth embodiment according to FIG.

  In the imaging optical system of Example 4, the phase plate PL is disposed close to the aperture stop S between the lens L3 and the aperture stop S of the imaging optical system of the “specific example”.

  Table 13 shows data of the imaging optical system of Example 4.

  Table 14 shows aspherical data of the phase modulation surface in the phase plate used in the imaging optical system of Example 4.

  FIG. 57 shows lateral aberrations, FIG. 58 shows longitudinal aberrations, and FIG. 59 shows curvature of field and distortion of the imaging optical system of Example 4.

  Further, the MTF of the imaging optical system of Example 4 is shown in FIGS. The subject distances corresponding to FIGS. 60, 61, and 62 are 370 mm, 400 mm, and 430 mm, respectively.

  FIG. 63 shows a kernel filter that is an image processing filter when the imaging optical system according to the fourth embodiment is used.

  As can be seen from the longitudinal aberration diagram of FIG. 58, the longitudinal aberration of the imaging optical system of Example 4 is that the longitudinal aberration diagram of Example 1 is “symmetrically switched”.

The object distance at this time: MSE, which is an “average value of mse” of 370 mm, 400 mm, and 430 mm, is 0.115, which is a lower value compared to Comparative Examples 1 and 2.
Therefore, even if the shape of the phase modulation surface of the phase plate in Examples 1 to 3 is a concave surface while maintaining the shape, the performance as the phase plate is hardly changed.

  In view of the above description, the phase modulation surface shape of the phase plate used in the imaging system of the present invention is summarized as follows.

  That is, the phase modulation surface has a rotationally symmetric aspheric shape, and is “monotonically increasing or decreasing monotonically from the center to the outer periphery” when the component due to the secondary aspheric term is removed.

Most sag amount is high (the lower) sag position 1, the maximum radius as _{h m,} sag ratio at the location of 0.75h _{m: Z} 0.75 / _{Z 0} is 0.55 to 0.67 Fits in range.

Most sag amount is high (the lower) sag position 1, the maximum radius as _{h m,} sag ratio at the position of 0.5h _{m: Z} 0.5 / _{Z 0} is 0.85-0.95 Fits in range.

  Further, when the phase plate is inserted in the vicinity of the aperture stop of the imaging optical system, the shape of the longitudinal aberration becomes characteristic.

  That is, as in the first, second, and fourth embodiments, “inclination gradually increases from the center of the pupil toward the outside of the pupil, passes through the image plane at about half of the outermost periphery of the pupil, and inflection points On the other hand, the spherical aberration becomes a shape in which the inclination is almost zero near the outermost periphery of the pupil.

  Alternatively, the spherical aberration has a “linear shape with a constant inclination” as in the third embodiment.

  The “imaging system” in which the embodiment has been described above is output from the imaging optical system 202 that images the imaging object 201, the imaging element 205 that captures an image of the imaging object by the imaging optical system, and the imaging element. And an image processing unit 206 that performs image processing on the image.

  The imaging optical system 202 includes an imaging optical system that forms an image of an imaging target, and a phase plate 203 that is added to the imaging optical system to increase the spherical aberration of the imaging optical system in order to increase the depth of focus. Have

  The image processing unit 206 performs “restoration processing on image data with increased spherical aberration” imaged by the imaging optical system.

  The phase plate 203 has a phase modulation surface of which one surface is a plane and the other surface is “a rotationally symmetric and aspherical shape with respect to the optical axis of the imaging optical system”.

The aspheric shape of this phase modulation surface is _expressed by the following equation: aspheric amount: Z, distance from rotational symmetry axis: h, normalized reference circular radius: H, n-order aspheric coefficient: an
Z = Σa _n (| h / H |) ⁿ (sum takes n = 2 to n = N for n)
In the aspheric shape represented by
Z-a ₂ (| h / H |) ²
However, it changes monotonously from h = 0 toward the outer peripheral side.

Further, the outermost radius to _{h m,} aspherical amount of the position of 0.75 h _m from h = _0: and _{Z 0.75,} the aspherical amount at h = 0: the ratio of the _{Z 0,} the condition:
(1) 0.55 ≦ Z _0.75 / Z ₀ ≦ 0.67
Satisfied.

Further, with respect to _{h m,} aspherical amount of the position of 0.5h _m: a _{Z 0.5,} aspherical amount at h = 0: the ratio of the _{Z 0,} the condition:
(2) 0.85 ≦ Z _0.5 / Z ₀ ≦ 0.94
Satisfied.

  The imaging system also includes an imaging optical system 202 that images the imaging object 201, an imaging element 205 that captures an image of the imaging object by the imaging optical system, and an image processing unit that performs image processing on an image output from the imaging element. 206 and has the following characteristics.

  That is, the imaging optical system includes an imaging optical system 202 that forms an image of the imaging target, and a phase that is added in the imaging optical system and increases the spherical aberration of the imaging optical system in order to increase the depth of focus. A plate 203 is provided.

  The phase plate 203 has one surface that is a plane and the other surface that has a rotationally symmetric and aspherical phase modulation surface with respect to the optical axis of the imaging optical system.

  The image processing unit 206 performs restoration processing based on an image processing filter: R (ω) on an image captured by the imaging optical system and having increased spherical aberration.

The image processing filter: R (ω) is obtained by OTF of the imaging optical system: H (ω), power spectrum of the imaging object: S (ω) ² , and power spectrum of noise peculiar to the imaging element: W (ω) ² The following formula:
(A) R (ω) = H (ω) ^* / [| H (ω) | ² + {S (ω) ² / W (ω) ² }]
Defined by

And R (ω), H (ω), S (ω) ² , W (ω) ² , the following formula:
(B) mse
= ∫ {| 1-R (ω) H (ω) | ² · | S (ω) | ² + | R (ω) | ² · | W (ω) | ² } dω
The average value of the maximum, intermediate, and minimum values of the subject distance within the depth of field of mse defined by: MSE is the condition:
(4) MSE <0.13
Satisfied.

Further, the filter gain: FG which is an average value for all frequencies of the image processing filter: R (ω) is a condition:
(5) FG <3.8
Satisfied.

The imaging optical system of the imaging optical system has an aperture stop 204, and a phase plate 203 having a phase modulation surface is disposed close to or in contact with the aperture stop 204, and the radius of the aperture stop is the outermost periphery of the aspherical surface. radius: substantially equal to _{h m.}

  The imaging optical system of the imaging optical system described in Examples 1 to 4 includes a positive first lens L1, a positive second lens L2, and a negative third lens in order from the object side to the image side. L3, an aperture stop 204, a negative fourth lens L4, a positive fifth lens L5, and a positive sixth lens L6 are arranged.

  The phase plate 203 is disposed on the object side of the aperture stop 204 and close to the aperture stop.

201 Object to be imaged (subject)
202 Imaging optical system
203 Phase plate
204 Aperture stop
205 Image sensor
206 Image processing unit
L1 positive first lens
L2 positive second lens
L3 negative third lens
S Aperture stop
L4 negative fourth lens
L5 positive fifth lens
L6 positive sixth lens

JP 2010-271689 A Japanese Patent No. 4377404

Claims (9)

An imaging optical system for imaging an imaging object;
An image sensor that captures an image of the object to be imaged by the imaging optical system;
In an imaging system having an image processing unit that performs image processing on image data output from the imaging device,
An imaging optical system includes an imaging optical system that forms an image of an imaging object, and a phase plate that is added to the imaging optical system and increases the spherical aberration of the imaging optical system in order to increase the depth of focus. Have
The image processing unit performs a restoration process on image data imaged by the imaging optical system and having increased spherical aberration,
The phase plate has one surface being a plane and the other surface having a rotationally symmetric and aspherical phase modulation surface with respect to the optical axis of the imaging optical system,
The aspherical shape of the phase modulation surface is
Aspherical amount: Z, the distance from the axis of rotational symmetry: h, normalized reference circle radius: H, n order aspheric coefficients: by a _n, wherein:
Z = Σa _n (| h / H |) ⁿ (sum takes n = 2 to n = N for n)
In the aspheric shape represented by
Z-a ₂ (| h / H |) ²
Changes monotonically from h = 0 toward the outer periphery,
Outermost radius to _{h m,} aspherical amount of the position of 0.75 h _m from h = _0: and _{Z 0.75,} the aspherical amount at h = 0: the ratio of the _{Z 0} is the condition:
(1) 0.55 ≦ Z _0.75 / Z ₀ ≦ 0.67
An imaging system characterized by satisfying The imaging system according to claim 1.
In the aspherical surface shape of the phase modulation surface, aspherical outermost radius to _{h m,} aspherical amount of the position of 0.5h _m from h = _0: and _{Z 0.5,} aspherical amount at h = 0 : the ratio of the _{Z 0} is, conditions:
(2) 0.85 ≦ Z _0.5 / Z ₀ ≦ 0.94
An imaging system characterized by satisfying An imaging optical system for imaging an imaging object;
An image sensor that captures an image of the object to be imaged by the imaging optical system;
In an imaging system having an image processing unit that performs image processing on image data output from the imaging device,
An imaging optical system includes an imaging optical system that forms an image of an imaging object, and a phase plate that is added to the imaging optical system and increases the spherical aberration of the imaging optical system in order to increase the depth of focus. Have
The phase plate has one surface being a plane and the other surface having a rotationally symmetric and aspherical phase modulation surface with respect to the optical axis of the imaging optical system,
The image processing unit performs a restoration process based on an image processing filter: R (ω) on an image captured by an imaging optical system and having an increased spherical aberration,
The image processing filter: R (ω) is obtained by OTF of the imaging optical system: H (ω), power spectrum of the imaging object: S (ω) ² , and power spectrum of noise peculiar to the imaging device: W (ω) ² The following formula: (A)
(A) R (ω) = H (ω) ^* / [| H (ω) | ² + {S (ω) ² / W (ω) ² }]
Is defined by
By the R (ω), H (ω), S (ω) ² , W (ω) ² , the following formula: (B)
(B) mse
= ∫ {| 1-R (ω) H (ω) | ² · | S (ω) | ² + | R (ω) | ² · | W (ω) | ² } dω
The average value of the maximum, intermediate, and minimum values of the subject distance within the depth of field of mse defined by: MSE is the condition:
(4) MSE <0.13
An imaging system characterized by satisfying The imaging system according to claim 3.
Image processing filter: Filter gain: FG which is an average value for all frequencies of R (ω) is:
(5) FG <3.8
An imaging system characterized by satisfying The imaging system according to claim 3 or 4,
The aspherical shape of the phase modulation surface of the phase plate is
Aspherical amount: Z, the distance from the axis of rotational symmetry: h, normalized reference circle radius: H, n order aspheric coefficients: by a _n, wherein:
Z = Σa _n (| h / H |) ⁿ (sum takes n = 2 to n = N for n)
In the aspheric shape represented by
Z-a ₂ (| h / H |) ²
Changes monotonically from h = 0 toward the outer periphery,
Outermost radius to _{h m,} aspherical amount of the position of 0.75 h _m from h = _0: and _{Z 0.75,} the aspherical amount at h = 0: the ratio of the _{Z 0} is the condition:
(1) 0.55 ≦ Z _0.75 /Z≦0.67
An imaging system characterized by satisfying The imaging system according to claim 5, wherein
In the aspherical surface shape of the phase modulation surface, aspherical outermost radius to _{h m,} aspherical amount of the position of 0.5h _m from h = _0: and _{Z 0.5,} aspherical amount at h = 0 : the ratio of the _{Z 0} is, conditions:
(2) 0.85 ≦ Z _0.5 /Z≦0.94
An imaging system characterized by satisfying In the imaging system according to claim 1 or 2 or 5 or 6,
The imaging optical system has an aperture stop,
Imaging system substantially equal to a h _m: a phase plate having a phase modulation surface, the is disposed close to or in contact with the aperture stop, the aperture stop radius, wherein the outermost aspheric radii. The imaging system according to any one of claims 1 to 7,
The imaging optical system includes, in order from the object side to the image side, a positive first lens, a positive second lens, a negative third lens, an aperture stop, a negative fourth lens, a positive fifth lens, a positive lens No. 6 lens,
A phase plate is disposed on the object side of the aperture stop in the vicinity of the aperture stop.   A phase plate used in the imaging system according to claim 1.

Images