JPH0580275A - Image pickup device - Google Patents

Abstract

PURPOSE:To provide the image pickup device which is inexpensive and has superior low-pass effect by providing at least one refracting surface which includes a point or line where a differentiation coefficient is discontinuous in an optical system and using a combination surface which includes at least one specific surface as this refracting surface. CONSTITUTION:This image pickup device is equipped with an optical system which forms an image on the image pickup surface of an image pickup element and provided with at least one surface including the point or line where the differentiation coefficient is discontinuous in the optical system; and this refracting surface is the combination surface which is expressed by an aspherical surface equation containing odd order shown by an equation I and has coefficients of terms of >=2th order so that at least one of the coefficient is not O, or contains at least one surface shown by the equation I. For example, luminous flux passing a part near an optical axis as shown in a figure is defocused by making its image formation position different from luminous flux passing a part at a distance from the optical axis and luminous flux split by the refracting surface forms a multiple image on the image pickup surface, so the low-pass effect operates, thereby preventing moire from being generated.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical system for forming an image on an image pickup surface of an image pickup device which samples the intensity of light on the image pickup surface to pick up an image.

[0002]

2. Description of the Related Art In recent years, an image pickup optical system using a solid-state image pickup device such as a CCD has been used for a device for picking up an image observed on a television monitor. The image pickup device used in these image pickup apparatuses samples the light intensity distribution on the image pickup surface at a certain frequency, converts the light intensity into an electric signal, and reproduces the electric signal on a television monitor.

However, when the image is reproduced by sampling in this way, only the frequencies up to the Nyquist limit can be reproduced by the sampling theorem. Further, near the Nyquist limit, a false resolution called "moiré" occurs.

For this reason, various measures have been taken to give the optical system a low-pass effect so that an image of a frequency near the Nyquist limit will not be resolved on the image pickup surface. For example, a method of making a double image by using a crystal filter or blurring an image by using a phase filter is well known.

Also, as disclosed in Japanese Utility Model Laid-Open No. 63-24523, a method of forming a double image by passing a part of a light beam through a wedge prism, and Japanese Patent Laid-Open No. 47-38001. As described in JP-A-63-6520, a method of forming an annular image with a conical prism as described in JP-A-63-6520, and high-order spherical aberration are generated to blur an image. There are ways.

[0006]

Of the above methods,
The method using a crystal filter, which is considered to be most widely used at present, provides a good low-pass effect because the point image is separated into two points. However, since the cutoff in the frequency space is one-dimensional, a plurality of crystal filters are usually used, which requires a large amount of space and is very expensive. In particular, when a sampled image of an image guide or the like is formed on the image pickup device, a large number of crystal filters are required, which makes it more expensive.

Further, the phase filter is inexpensive but generally inferior in performance to the crystal filter.

The method using the wedge prism also has the same drawbacks as using the crystal filter because the point image separation is one-dimensional.

The method of utilizing higher-order spherical aberration is relatively inexpensive and can obtain a two-dimensional low-pass effect. However, light rays near the optical axis are not much affected by higher-order aberrations. Therefore, high-frequency components cannot be completely removed, and it is difficult to obtain a good low-pass effect as a crystal filter.

Further, the conical prism has a two-dimensional low-pass effect, does not require a space like a wedge prism and a crystal filter, and the light beam near the optical axis is also separated by the prism, so that it is a high-order spherical surface. High-frequency components do not remain unlike the method using aberration. However, due to defocusing, the diameter of the minimum circle of confusion hardly changes, the intensity at the center of the point image intensity distribution increases, and as a result, the MTF increases, and a good low-pass effect cannot be obtained. Also, good point image separation cannot be obtained due to the aberration of the optical system.

An object of the present invention is to provide an image pickup apparatus equipped with an optical system having a refracting surface which is inexpensive and which can obtain an excellent low-pass effect.

[0012]

An image pickup apparatus according to the present invention comprises an optical system for forming an image on the image pickup surface of an image pickup element for sampling the light intensity on the image pickup surface and picking up the image. At least one refracting surface including a point (or line) having a discontinuous differential coefficient is provided therein, and the refracting surface including a point (or line) having a discontinuous differential coefficient is z in the optical axis direction, When the vertical direction is defined as r, it is represented by an aspherical expression including an odd order shown in the following expression (1), and at least one of the coefficients of the second and higher terms is not 0, or the expression ( It is represented by a combination surface containing at least one aspherical expression including an odd order shown in 1). z = C ₀ + C ₁ r + C ₂ r ² + C ₃ r ³ + ... + C _n r ⁿ (C ₁ ≠ 0) (1) where r ² = x ² + y ² and r ≧ 0.

The apparatus of the present invention has a structure as shown in FIG. 1, for example, 1 is an eyepiece which is a part of an endoscope including an eyepiece 1a, and 2 is an adapter including the above optical system. Three
Is a television camera, 4 is an image pickup surface, and 5 is a cover glass. In the embodiment shown in FIG. 1, the refraction surface is formed on the cover glass. Reference numerals 6 and 7 are a crystal filter and an infrared cut filter, respectively.

A refracting surface including a point (or line) having a discontinuous differential coefficient provided in an optical system included in the apparatus of the present invention is disclosed in Japanese Patent Application Laid-open No. 47-38001. Unlike a wedge prism or a conical prism, for example, as shown in FIG. 3, it is a refraction surface having a shape in which the central portion and the peripheral portion of the surface have different differential coefficients.

As shown in FIG. 15, in the prism disclosed in the above-mentioned publication, as shown in FIG. 16, the ring-shaped intensity distribution does not change the diameter of the ring zone due to defocusing, and the intensity of the central portion of the ring zone is small. MTF goes up because it increases. In general, when adjusting the focus, the focus is adjusted to the best resolution, so that a good cutoff cannot be obtained and moire occurs.

On the other hand, in the apparatus of the present invention, the refracting surface as described above is arranged so that, for example, as shown in FIG. 4, a light beam passing through a portion near the optical axis and a light beam passing through a portion far from the optical axis are provided. Defocusing is caused by changing the image forming position, so that the MTF does not rise.

The surface shape as described above is generally represented by a combination of a plurality of polynomial aspherical surfaces. In addition, it may be expressed by an aspherical expression including an odd order, and is expressed by the above expression (1).

In the above equation (1), when C ≠ 0, the condition is that the surfaces are not connected smoothly on the optical axis, that is, the differential coefficients of the surfaces include discontinuous points or lines. Also C
_{When n} (n ≧ 2) is all 0, the equation (1) becomes a straight line, but if one or more terms are not 0, it becomes a curve in general and the degree of freedom in design for obtaining an optimum separated image increases. preferable. As a result, the MTF of the image formed on the image pickup surface is near the Nyquist limit of the image pickup element or is provided with a sampling image transmission system such as an image guide. The image transmitted by this sampling image transmission system is displayed on the image pickup element. In the case of forming an image at, the cutoff may be made at any of the vicinity of the frequency of the projected image on the image pickup device of the sampling image transmission system.

Since the light beam divided by the refracting surface forms a multiple image (or an annular image) on the image pickup surface, a low-pass effect works and moire can be prevented. The conditions for causing the ring zone image to have a cutoff at the Nyquist limit at this time are as follows. a≈0.77p where a is the radius of the ring zone, and p is the sampling pitch of the image sensor.

Therefore, the inclination angle θ of the refracting surface near the optical axis
Can be expressed by the following formula. | Θ | = a / {f ₂ · (n−1)} = {2 · f _n · f ₂ · (n−1)} ⁻¹ where n is the refractive index of the medium and θ is (A) in FIG. , (B), the inclination angle near the optical axis of the refracting surface including the discontinuous point (or line), which is usually a small angle, sin θ≈θ, f _n
Is the Nyquist limit (f _n = 1 / 2p) of the image sensor or the sampling image transmission system, and f ₂ is the focal length of the optical system between the refractive surface including the point (or line) having a discontinuous differential coefficient and the image sensor. Is.

At this time, θ represents only the relationship between the light beam near the optical axis and the Nyquist limit, and does not represent the cutoff frequency of the entire optical system, but even considering the aberration generated in the optical system, It is desirable that θ satisfies the following expression (2). {0.2 · f _n · f ₂ · (n-1)} ⁻¹ ≧ | θ | ≧ {10 · f _n · f ₂ · (n-1)} ⁻¹ (2) Normally, θ is very small. In the case of an optical system having a small pupil diameter, the height of the surface ridge or the depth of the indentation becomes very small, which makes it difficult to manufacture, and accuracy may not be ensured due to variations. In such a case, if the refracting surface including the point (or line) having the discontinuous differential coefficient is a joint surface with a flat surface or a curved surface, (n-1) of the equation (2) becomes (n
-N _b ), and the value of θ becomes large, it is desirable that the height of the surface ridge or the depth of the depression can be increased. Incidentally n _b is the refractive index of the adhesive.

Further, between θ and C ₁ in the equation (1),
The following relationships are established. C ₁ = tan θ≈θ Furthermore, it is desirable to arrange a refracting surface including a point (or line) having a discontinuous differential coefficient in the vicinity of the pupil so that a good low-pass effect can be obtained over the entire screen. At this time, the refraction surface including the point (or line) having the discontinuous differential coefficient or the prism (lens) including the refraction surface may be slightly decentered with respect to the optical axis. Even if it is slightly eccentric near the pupil, it does not significantly affect the separation of point images,
This is because it also prevents ghosts.

A point (or line) where the differential coefficient is discontinuous
If the refracting surface containing is rotationally symmetric, the MTF can be operated two-dimensionally, and the number of low-pass filters can be reduced.

When using image pickup devices having different Nyquist limits in the horizontal direction and the vertical direction, a single low-pass filter is used to vertically and horizontally by using an anamorphic low-pass filter as shown in FIG. A cutoff can be given near the Nyquist limit in the direction, which is effective. In FIG. 6, when the optical axis direction is the z axis, (A) is an yz section (vertical section), and (B) is an xz section (horizontal section). This anamorphic surface is expressed by the following equation. z = A ₀ + A ₁ x + B ₁ y + A ₂ x ² + B ₂ y ² + A ₃ x ³ + B ₃ y ³ + ... A _n x ⁿ + B _n y ⁿ (A ₁ ≠ 0 or B ₁ ≠ 0) The above refraction The surface may be rotated around the optical axis for use, if desired.

In the case of a system for observing an image on a television monitor by attaching a television camera to the fiberscope,
In general, since the image guide differs depending on the fiberscope, the frequency of the image guide formed on the image pickup device of the television camera differs. Therefore, it is difficult to remove moire from all the fiberscopes used.

In the system as described above, it is desirable to use the optimum low-pass filter according to the combination of the fiberscope and the television camera. For that purpose, for example, the adapter for connecting the fiberscope and the television camera can be exchanged, and the low-pass filter of the present invention matching the frequency of the image guide may be arranged in the adapter. Further, a low pass filter suitable for the image fiber may be arranged in the fiber scope.

When a rigid scope equipped with a relay lens and a fiberscope are used in the same system, if a low-pass filter for the fiberscope is used in the rigid scope, the image quality will be degraded more than necessary. On the contrary, if a low-pass filter for a rigid endoscope is used in combination with a fiberscope, moire will occur.

Therefore, if the low-pass filter of the present invention can be replaced or the adapter including the low-pass filter of the present invention can be replaced, the rigid endoscope and the fiberscope can be used with optimum image quality in the same system. It will be possible. Furthermore, if the moire removing filter of the present invention, which is arranged in the adapter or the television camera, is replaceably arranged, an inexpensive and optimum system can be obtained.

The low-pass filter of the present invention can be used simultaneously with a plurality of filters, or can be used in combination with another low-pass filter such as a crystal filter. This is because the required low-pass effect differs depending on the system used, and especially when an image sampled by an image guide or the like is formed on the image sensor, the sampling frequency is different, so many low-pass filters are used. This is because it costs. For example, in a color mosaic filter-equipped CCD or the like, the frequency at which moire occurs has directionality. Therefore, near the sampling frequency of the color in the horizontal direction where strong moire is generated, the MTF is dropped by the crystal filter, and the sampling frequency of the 6-direction dense image guide is the same phase in 60 ° steps, so the MTF is reduced by the low-pass filter according to the present invention. It is effective if dropped, and the relationship between the fiber-to-fiber distance φ of the image guide and C ₁ can be expressed by the following equation. 0.5 × φ × sin (π / 3) × β = C ₁ × f ₂ × (n−1) × 2 where β is the projection magnification on the image sensor. Also, as mentioned above, when the low-pass filter (refractive surface) is the joint surface,
In the above equation, (n-1) becomes (n- _nb ).

Since the low-pass effect is also affected by the aberration of the optical system, the value of C ₁ does not need to strictly satisfy the above expression, and in practice, the following expression may be satisfied. 5 × φ × sin (π / 3) × β = C ₁ × f ₂ × (n-1) × 2 ≧ 0.1 × φ × sin (π / 3) × β Further, the low-pass filter of the present invention is integrated with a lens. If it is realized, the price will decrease further, which is desirable.

[0031]

EXAMPLES Next, examples of the present invention will be shown.

FIG. 1 shows the configuration of an embodiment of the present invention. For example, an adapter 2 detachably arranged between an endoscope (eyepiece 1) and a television camera 3 The mirror TV adapter uses a rotationally symmetric low-pass filter having the cross-sectional shape shown in FIG. This Figure 7
The low-pass filter shown in (1) is preferable because the surface other than on the optical axis is smooth so that light scattering is small and flare does not easily occur.

A crystal filter having a trap line 10 as shown in FIG. 8 or 9 is arranged in the television camera 3. The low-pass filter of the optical element in the adapter is the first lens (cover glass), and the refracting surface thereof is an aspherical surface having an aspherical shape including odd orders. The trap line in the frequency space on the image pickup surface by this low-pass filter coincides with the sampling frequency of the image guide end surface projected on the image pickup surface, as shown in FIG. In the figure, 11 is a sampling point of the image guide, and 12 is a top line.

With such a configuration, it is desirable that even when combined with endoscopes having different sampling frequencies, it can be combined with an adapter having an optimum cutoff frequency. If the low-pass filter (cover glass) can be replaced, it is more desirable because one adapter can be used for multiple endoscopes.

The adapter of this embodiment has a zoom function, and the sampling frequency of the image guide on the image pickup surface is changed by zooming. In this case, if the low-pass filter is placed in front of the variable power optical system, the sampling frequency of the image guide on the imaging surface and the top line of the low-pass filter will always match, and moire will be less likely to occur at any magnification. It can be a system.

11 and 12 show MTFs at the wide end and the tele end of the first embodiment, respectively. However, the crystal filter is not considered.

The low-pass filter used in this embodiment is not limited to the one shown in FIG. 7 above, but also FIGS.
The one shown in is used. Also, a low-pass filter as shown in FIG. 14 can be considered.

FIG. 2 shows the configuration of the second embodiment of the present invention.
This embodiment is an example in which the refracting surface is provided after the stop in the objective lens of the television camera, and any type of low-pass filter shown in FIGS. 3, 6, and 7 may be used.

Next, the data of the low-pass filters used in Example 1 and this Example are shown. Example 1 f = 22.636~42.793, F / 4.9 ~9.3, object distance = -1000 r ₁ = ∞ _{(stop) d 1 = 0.484 r 2 =} ∞ d 2 = 0.8 n 2 = 1.51633 ν 2 = 64.15 r 3 = ∞ d ₃ = 2.8 r ₄ = ∞ d ₄ = 1 n ₄ = 1.51633 ν ₄ = 64.15 r ₅ = ∞ d ₅ = 3.1 r ₆ = 1.71 d ₆ = 1.37 n ₆ = 1.72 ν ₆ = 50.25 r ₇ = -13.71 _{d 7 = 1 n 7 = 1.78472} ν 7 = 25.71 r 8 = ∞ d 8 = 5.134 ~7.703 r 9 = -6.812 d 9 = 1.5 n 9 = 1.84666 ν 9 = 23.78 r 10 = -3.705 d 10 = 0.8 n 10 = 1.62374 ν ₁₀ ＝ 47.1 r ₁₁ ＝ 8.719 d ₁₁ ＝ 7.527 〜1.251 r ₁₂ ＝ 18.929 d ₁₂ ＝ 2.76 n ₁₂ ＝ 1.62041 ν ₁₂ ＝ 60.06 r ₁₃ ＝ -13.442 d ₁₃ ＝ 0.2 r ₁₄ ＝ 9.197 d ₁₄ ＝ 4.71 n ₁₄ = 1.51633 ν ₁₄ = 64.15 r ₁₅ = -9.197 d ₁₅ = 0.8 n ₁₅ = 1.85026 ν ₁₅ = 32.28 r ₁₆ = 23.081 d ₁₆ = 2.171 to 5.879 r ₁₇ = ∞ d ₁₇ = 1 n ₁₇ = 1.51633 ν ₁₇ = 64.15 r ₁₈ = ∞ Shape of refraction surface (r ₅ ) (A) [corresponding to FIG. 3 Low pass filter data] 0 <r ≤ 1, C ₀ = 0, C ₁ = 8.2 × 10 ^-4 , 1 <r ≤ 2 C ₀ = 8.2 × 10 ^-4 , C ₁ = -8.2 × 10 ^-4 ( B) [Data 1 of low-pass filter corresponding to FIG. 7] 0 <r ≦ 2.2, C ₀ = 0, C ₁ = 6.21340780482349713 × 10 ⁻⁴ C ₂ = −1.11831431665536618 × 10 ⁻³ , C ₃ = 1.72326254774251052 × 10 ^{− 2} C ₄ = -7.4947015797950739 × 10 ^-2 , C ₅ = 0.15375365501776678 C ₆ = -0.17470277510871939, C ₇ = 0.11630783747263494 C ₈ = -4.52714464390924533 × 10 ^-2 , C ₉ = 9.56245557825196896 × 10 ^-3 C ₁₀ = -8.481108546 ^-4 (C) [data 2 of low-pass filter corresponding to FIG. 7] 0 <r ≦ 1.9, C ₀ = 0, C ₁ = 6.98116188060607758 × 10 ⁻⁴ C ₂ = 3.16776369268199085 × 10 ⁻⁵ , C ₃ = −2.53997915527410557 × 10 ^-4 C ₄ = 1.69910819567360878 × 10 ^-3 , C ₅ = -1.00618592831366177 × 10 ^-2 C ₆ = 2.59231882276316659 × 10 ^-2 , C ₇ = -3.1762710880 5453862 × 10 ^-2 C ₈ = 1.9706279862760988 × 10 ^-2 , C ₉ = -6.001906185353107658 × 10 ^-3 C ₁₀ = 7.21487026929249018 × 10 ^-4 (D) [low pass filter data 3 corresponding to Fig. 7] 0 <r ≤ _{1.9, C 0 = 0, C} 1 = 5.98410923155050407 × 10 -4 C 2 = 2.67892063030759041 × 10 -5, C 3 = -2.15027456191388931 × 10 -4 C 4 = 1.4457242736981412 × 10 -3, C 5 = -8.60047940280224323 × 10 - ³ C ₆ = 2.21876770919958392 × 10 ^-2 , C ₇ = -2.7198850592359095 × 10 ^-2 C ₈ = 1.6878252736166768 × 10 ^-2 , C ₉ = -5.15576206337112989 × 10 ^-3 C ₁₀ = 6.180304607001828 × 10 ^-4 (E) [Fig. 7 data of low-pass filter 4] 0 <r ≦ 2.2, C ₀ = 0, C ₁ = 5.99973411495760274 × 10 ⁻⁴ C ₂ = 7.24078912223179768 × 10 ⁻⁷ , C ₃ = −9.50298609445933418 × 10 ⁻⁶ C ₄ = 1.28239522689032291 × 10 ^-4 , C ₅ = -1.09084425624676046 × 10 ^-3 C ₆ = 3.41265021400184634 × 10 ^-3 , C ₇ = -4.60857251099639799 × 10 ^-3 C ₈ = 2.9131337750895013 × 10 ^-3 , C ₉ = -8.65112114233603337 × 10 ^-4 C ₁₀ = 9.80516170458266827 × 10 ^-5 (F) [data 5 of the low-pass filter corresponding to Fig. 7] 0 <r ≤ 2.2, C ₀ = _{0, C 1 = -6.21386025668877481 × 10} -4 C 2 = 1.11903042234138932 × 10 -3, C 3 = -1.72370859561942237 × 10 -2 C 4 = 7.49614215496832575 × 10 -2, C 5 = -0.153780579745271 C 6 = 0.17473340572566055, C 7 = -0.1163293334441247 C ₈ = 4.52805238737387303 × 10 ^-2 , C ₉ = -9.56456858123039266 × 10 ^-3 C ₁₀ = 8.48319025793002385 × 10 ^-4 (G) [low pass filter data 6 corresponding to FIG. 7] 0 <r ≦ 1.9, _{C 0 = 0, C 1 =} 7.29467950111891425 × 10 -4 C 2 = -7.20406256342096506 × 10 -3, C 3 = 0.11227931692366647 C 4 = -0.48029263512608256, C 5 = 0.97855628529132503 C 6 = -1.1214666672199971, C 7 = 0.76512149197889504 C 8 = _{-0.30918978501733992, C 9 = 6.84811578855889364 × 10} -2 ^{_{10 = -6.41739833484116645 × 10 -3 (H}} ) [ data of the low-pass filter corresponding to FIG. 6] 0 <r ≦ 1, A 0 = 0, A 1 = 0.5 × 10 -3, B 1 = 0.45 × 10 -3 1 <r ≦ 2, A ₀ = z (when x ² + y ² = 1), A ₁ = −0.5 × 10 ⁻³ B ₁ = −0.45 × 10 ⁻³ (I) [low-pass filter corresponding to FIG. 13] Data] 0 <r ≦ 2.2, C ₀ = 0, C ₁ = 1.18202302586474311 × 10 ⁻³ C ₂ = 1.02432495935523004 × 10 ⁻³ , C ₃ = −6.20002963466144939 × 10 ⁻³ C ₄ = 1.52073827862137124 × 10 ⁻² , C ₅ = -1.888737777155327342 x 10 ^-2 C ₆ = 1.30665516375023426 x 10 ^-2 , C ₇ = -5.332356937854670548 x 10 ^-3 C ₈ = 1.27413320587890262 x 10 ^-3 , C ₉ = -1.666204863233887403 x 10 ^-4 C ₁₀ = 9.1386676289853178 x 10 ^{-6 In the} above data, r ₁ , r ₂ , ... Are the radii of curvature of each surface,
d ₁ , d ₂ , ... are surface distances, n ₁ , n ₂ , ... are refractive indices of a medium such as a lens, and ν ₁ , ν ₂ , ... Are similarly Abbe numbers. Further, r ₅ is a refracting surface including points (or lines) having discontinuous differential coefficients, and r _{1 to} r ₃ are data on the exit end side of the endoscope.

The pixel pitch of the image sensor of the above embodiment is Px
= 0.0096 (horizontal direction) and Py = 0.0099 (vertical direction).

Nine kinds of (A) to (I) are shown as examples of the refracting surface of the low-pass filter used, and all of them show good low-pass effect.

[0042]

The image pickup apparatus of the present invention uses an inexpensive lowpass filter, and can obtain an optimum lowpass effect according to the system used.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of a first embodiment of the present invention.

FIG. 2 is a diagram showing a configuration of a second embodiment of the present invention.

FIG. 3 is a sectional view of a low-pass filter used in the present invention.

FIG. 4 is a diagram showing a state of image formation when the low pass filter is used.

FIG. 5 is a diagram showing a tilt angle near a discontinuity point of the low-pass filter.

FIG. 6 is a sectional view of another low-pass filter used in the present invention.

FIG. 7 is a sectional view of another low-pass filter used in Example 1 of the present invention.

FIG. 8 is a diagram showing a top line of a crystal filter arranged in a TV camera.

FIG. 9 is a diagram showing a top line of another crystal filter arranged in the television camera.

FIG. 10 is a diagram showing a top line of a low-pass filter used in the present invention.

FIG. 11 is a diagram showing MTF at the wide end according to the first embodiment.

FIG. 12 is a diagram showing MTF at the telephoto end according to the first embodiment.

FIG. 13 is a diagram of another low-pass filter used in the present invention.

FIG. 14 is a diagram of still another low-pass filter used in the present invention.

FIG. 15 is a diagram showing a state of image formation when a conventional wedge prism is used.

FIG. 16 is a diagram showing a spatial frequency characteristic when the prism is used.

Claims (1)

[Claims] 1. An image pickup apparatus including an optical system for forming an image on an image pickup surface of an image pickup element for sampling light intensity and picking up an image, wherein a refracting surface including points or lines having discontinuous differential coefficients in the optical system. With at least one surface, where the refracting surface has an optical axis direction z and a direction perpendicular to the optical axis is r, the following formula (1)
And at least one of secondary and higher-order terms in the formula (1) is not 0, or is a combined surface including at least one surface represented by the formula (1). apparatus. z = C ₀ + C ₁ r + C ₂ r ² + C ₃ r ³ + ... + C _n r ⁿ (C ₁ ≠ 0) (1) where r ² = x ² + y ² and r ≧ 0.