JP5480070B2 - Front converter and zoom lens inspection method and apparatus using the same - Google Patents

Description

  The present invention relates to a front converter used for inspection of a zoom lens.

  The present invention also relates to a zoom lens inspection method and apparatus using such a front converter.

  Conventionally, when inspecting a zoom lens, a resolution chart is used as a subject, an image of the chart is formed by a lens to be examined, and the image is observed by a microscope, and the imaging performance is inspected, or the image A method has been used in which imaging performance is inspected based on an electrical signal output by a photoelectric conversion element that has captured the image.

  Conversely, a resolution chart is placed at the imaging position in the above case, and it is back projected onto the subject side (the chart side in the above case) by the test lens, and the projected chart image is visually observed. A method for inspecting image performance is also commonly used.

  However, in recent years, as the focal length on the telephoto side has become longer due to the higher magnification of the zoom lens, the variation in aberration due to the subject distance becomes larger on the telephoto side, which increases the distance from the resolution chart to the lens to be examined. As a result, the problem of enlarging inspection facilities has arisen. The same applies to the case where the resolution chart is projected by the test lens. In this case, the distance from the test lens to the projection surface becomes longer.

  In order to solve this problem, for example, by inserting a close-up lens as shown in Patent Documents 1 and 2, a resolution chart or a method in which the distance between the projection surface and the test lens can be shortened for inspection Are also known in the art.

JP 7-318801 A JP 2002-6213 A

  However, in order to perform inspection with sufficiently small equipment, the method using a close-up lens makes it difficult to produce such a chart with sufficient accuracy because the chart becomes too fine. . Also, when performing the above-described back projection, a problem has been recognized that the projection image becomes too small and it becomes difficult to discriminate details.

  The present invention has been made in view of the above problems, and provides a zoom lens inspection method capable of performing high-precision inspection after setting a resolution chart or a distance between a projection surface and a lens to be measured short. It is intended to do.

  It is another object of the present invention to provide a zoom lens inspection apparatus capable of performing such an inspection method.

  A further object of the present invention is to provide a front converter capable of realizing such a zoom lens inspection method and apparatus.

The front converter according to the present invention is
As described above, the front converter is used for inspecting the zoom lens by forming or projecting a resolution chart with a zoom lens as a subject,
In a front converter disposed between a resolution chart when the image is formed or a projection surface when the projection is performed and a zoom lens set to a state other than the wide-angle end,
In order from the opposite side to the zoom lens, a front group composed of only cemented lenses and having negative refractive power, and a rear group composed of only cemented lenses and having positive refractive power are disposed.
It has an angular magnification of less than 1.

On the other hand, the inspection method of the zoom lens according to the present invention is:
In the zoom lens inspection method for inspecting the zoom lens by forming or projecting a resolution chart with the zoom lens as a subject as described above,
A front converter having an angular magnification of less than 1 is disposed between a resolution chart when the image is formed or a projection surface when the projection is performed and a zoom lens set to a state other than the wide-angle end. It is characterized by this.

  The “inspection method” in the present invention is not only a normal inspection for evaluating and discriminating the performance of the zoom lens, but also the image of the resolution chart is projected or projected, and the zoom lens is adjusted while observing it (see FIG. For example, it includes operations for adjusting the eccentricity, tilting, and focus state of the lens. In other words, even in this type of adjustment work, how to adjust the lens is naturally decided according to the evaluation and discrimination of the performance of the zoom lens, so that the work includes the inspection of the zoom lens. Is self-explanatory.

The zoom lens inspection apparatus according to the present invention for carrying out the above method is
In a zoom lens inspection apparatus in which a resolution chart is formed or projected by the zoom lens in order to use the zoom lens for inspection,
A front converter having an angular magnification of less than 1 is disposed between a resolution chart when the image is formed or a projection surface when the projection is performed and a zoom lens set to a state other than the wide-angle end. It is characterized by that.

More specifically, also in the zoom lens inspection method of the present invention, the front converter having an angular magnification of less than 1 described above is composed of only a cemented lens in order from the opposite side to the zoom lens and has a negative refractive power. A front converter comprising a front group having a positive lens and a rear group having a positive refractive power is used.

Also in the zoom lens inspection apparatus of the present invention, more specifically, as a front converter having an angular magnification of less than 1 as described above, the front converter is composed of only a cemented lens in order from the opposite side to the zoom lens and has a negative refractive power. A front converter having a front group having a positive lens and a rear group having a positive refractive power is applied.

  In the present invention, the Abbe number of the positive lens constituting the front group of the front converter is ν1p, the Abbe number of the negative lens is ν1n, the Abbe number of the positive lens constituting the rear group is ν2p, and the Abbe number of the negative lens Is preferably ν2n, the following equation should be satisfied.

ν1p <ν1n (1)
ν2p> ν2n (2)
Furthermore, in the present invention, it is desirable that the opposite surface has a smaller absolute value of the paraxial curvature radius than the surface of the front lens side of the cemented lens constituting the rear group of the front converter. .

  In the present invention, the back magnification (distance from the rearmost vertex of the lens to the rear focal point of the lens) when the angular magnification of the front converter is γ and the distance from the resolution chart when the image is formed to the front converter is 1000 mm. ) Is fb, it is desirable that the following formula is satisfied.

0.1 <γ <0.9 (3)
−0.25 <1000 / fb (4)
The values of the angular magnification γ and the back focus fb are more preferably set within a range that satisfies the following expression.

0.2 <γ <0.9 (3) ′
−0.25 <1000 / fb <0.2 (4) ′
In the present invention, in order to reduce the influence on the performance due to the manufacturing error of the front converter, it is desirable that all the surfaces of the lens constituting the front converter are formed of spherical surfaces. However, the present invention is not limited to this, and a part of the surface of the lens may be composed of an aspherical surface.

  In order to accurately inspect a zoom lens having a long focal length on the telephoto side, a resolution chart or projection image of a certain size is required. However, if the inspection distance is shortened to make the equipment smaller, the resolution chart or the projected image also becomes smaller. Therefore, it is conceivable to use the front wide converter together with the close-up lens described in Patent Documents 1 and 2 described above to enable inspection on the telephoto side while using a sufficiently large chart. Such wide converters are disclosed in, for example, Japanese Patent Application Laid-Open Nos. 2006-119346, 2006-39102, 2006-84811, 2007-178826, and Japanese Patent Application Laid-Open No. 63-1000041. There is a description. However, when the close-up lens and the front wide converter are used in combination, the inspection optical system becomes complicated, which leads to a decrease in inspection accuracy, which is not preferable.

  Based on the above knowledge, the present invention achieves downsizing of the inspection apparatus without reducing the inspection accuracy by combining the front wide converter with the function of a close-up lens. That is, the front converter according to the present invention has an angular magnification of less than 1, so that when a finite inspection distance (resolving power chart or distance between the projection surface and the zoom lens) is set, the inspection is performed. It is possible to ensure high inspection accuracy by forming a virtual image at a distance farther than the distance. Therefore, according to the present invention, it is possible to inspect the telephoto side in a small space even for a zoom lens with a high magnification.

  On the other hand, the conventional front wide converter has an angular magnification of less than 1, but since it is an afocal system, when it is applied, it is not possible to shorten the inspection distance in order to ensure high inspection accuracy. .

  Further, according to the present invention, it is possible to obtain an effect of reducing the influence of air fluctuation by shortening the inspection distance. If the inspection distance can be shortened as described above, it is easy to mount the lens to be tested and the front converter on the same frame. By doing so, the equivalent focal length of the optical system that combines the lens to be examined and the front converter can be shortened, and the influence of vibration can be reduced. The influence of the air fluctuation and vibration is a serious problem in the inspection of the long focal length lens. Therefore, it can be said that the practical value is extremely high in eliminating this influence.

  Here, it is not sufficient for the front converter of the present invention used for the above-mentioned purpose to obtain good performance in combination with the zoom lens of the subject. That is, it is important that the performance of the zoom lens is hardly changed, and the performance of the zoom lens should not be greatly changed due to a manufacturing error of the front converter. Furthermore, sufficient tolerance is required for the relative positional relationship with the zoom lens.

From this point, the front converter of the present invention is configured such that a front group having a negative refractive power and a rear group having a positive refractive power are arranged in this order from the opposite side to the zoom lens that is the subject . With such a configuration, the assembly of the front converter is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

Then, the front group and the rear group as described above is particularly, since both are composed of only a cemented lens, the generation of the lens assembly errors in each group is suppressed, to the lens performance due to the assembly error The influence can be eliminated.

  In the present invention, it is easy to correct chromatic aberration of magnification particularly when the front converter satisfies the expression (1), and to correct axial chromatic aberration when the expression (2) is satisfied. Will also be easier.

  In the present invention, particularly when the opposite surface has a smaller absolute value of the paraxial radius of curvature than the surface on the front group side of the cemented lens constituting the rear group of the front converter, the aberration This is advantageous in terms of correction. That is, when the front converter is used for the inspection of the zoom lens as in the method of the present invention, the distortion aberration can be ignored, and it is necessary to mainly correct spherical aberration, coma aberration, astigmatism, and chromatic aberration. Therefore, if the cemented lens constituting the rear group is configured as described above, it is possible to easily correct each of the above-mentioned aberrations other than the chromatic aberration that needs to be corrected while ensuring the necessary angular magnification.

  In the present invention, in particular, when the front converter satisfies the expressions (3) and (4), it is possible to construct an inspection system with high inspection accuracy.

  That is, the expression (3) defines a preferable range of the angular magnification γ. When the angular magnification γ is equal to or lower than the lower limit defined therein, the aberration due to the front converter increases, and the performance of the lens to be measured is reduced. It becomes difficult to judge accurately. Further, when the angular magnification γ exceeds the upper limit defined therein, the function of the front converter as a wide converter becomes weak, and it becomes impossible to sufficiently increase the resolution chart or the projected image. That is, if the expression (3) is satisfied, the aberration due to the front converter can be suppressed, and the resolution chart or the projected image can be made sufficiently large to increase the inspection accuracy.

  When the front converter satisfies the above expression (3) ′, the lower limit of the angular magnification γ becomes larger, so that the effect of suppressing the above-described aberration becomes greater.

  On the other hand, equation (4) shows the conditions for shortening the inspection distance. When the value of 1000 / fb falls below the lower limit specified therein, the function as a close-up lens is weakened, and the inspection distance is sufficiently set. It cannot be shortened. Here, a value at a subject distance (inspection distance) of 1000 mm is typically used here, but it is desirable that the actual inspection distance is closer than that in order to reduce the size of the apparatus. In order to form a virtual image at a far distance with an inspection distance shorter than 1000 mm, equation (4) can take a positive value.

  Further, when the front converter satisfies the expression (4) ′, the position accuracy of the front converter is relaxed. That is, when the value of 1000 / fb is equal to or greater than the upper limit defined therein, the refractive power of the close-up lens becomes too strong, and it becomes difficult to ensure positional accuracy.

1 is a perspective view showing a schematic configuration of a zoom lens inspection apparatus according to an embodiment of the present invention. Sectional drawing which shows the optical system of Example 1 in the inspection apparatus of the zoom lens by this invention Sectional drawing which shows the optical system of Example 2 in the inspection apparatus of the zoom lens by this invention Sectional drawing which shows the optical system of Example 3 in the inspection apparatus of the zoom lens by this invention Sectional drawing which shows the optical system of Example 4 in the inspection apparatus of the zoom lens by this invention Sectional drawing which shows the optical system of Example 5 in the inspection apparatus of the zoom lens by this invention Sectional drawing which expands and shows a part of optical system of FIG. Sectional drawing which shows the optical system of Example 6 in the inspection apparatus of the zoom lens by this invention Sectional drawing which expands and shows a part of optical system of FIG. Sectional drawing which shows the optical system of Example 7 in the inspection apparatus of the zoom lens by this invention Sectional drawing which shows the optical system of Example 8 in the inspection apparatus of the zoom lens by this invention (A) to (D) are aberration diagrams of only the zoom lens of Example 1, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined. (A) to (D) are aberration diagrams of only the zoom lens of Example 2, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined. (A) to (D) are aberration diagrams of the zoom lens only of the third embodiment, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined. (A) to (D) are aberration diagrams of only the zoom lens of Example 4, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined. (A) to (D) are aberration diagrams of only the zoom lens of Example 5, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined. (A) to (D) are aberration diagrams of only the zoom lens of Example 6, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined. (A) to (D) are aberration diagrams of the zoom lens only of the seventh embodiment, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined. (A) to (D) are aberration diagrams of only the zoom lens of Example 8, and (E) to (H) are aberration diagrams of an optical system in which the zoom lens and the front converter are combined.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a schematic perspective view of a zoom lens inspection apparatus according to an embodiment of the present invention. As shown here, a conventionally known resolving power chart 1 is arranged at a predetermined position, and an image of the resolving power chart 1 is formed by a zoom lens 2 and a front converter 3 as test lenses. At this time, the zoom lens 2 is set to a state other than the wide-angle end, and in many cases, to the telephoto end. The formed image is picked up by an image pickup device 4 such as a CCD image pickup device, and an electric image signal Sd carrying the image is output from the image pickup device 4. Since the image signal Sd indicates the sharpness and distortion of the image, the performance of the zoom lens 2 can be inspected by subjecting the image signal Sd to predetermined processing.

  In addition to inspecting the performance of the zoom lens 2 based on the image signal Sd as described above, the zoom lens 2 can also be inspected by the inspector magnifying and observing the formed image with a microscope or the like. . On the other hand, a resolution chart is arranged at the position of the image pickup element 4, and is projected onto the resolution chart 1 side in the above case by the zoom lens 2 and the front converter 3, and the projection image is observed, for example. It is also possible to perform two inspections.

  As described above, the front converter 3 is installed to enable high-precision inspection while shortening the inspection distance, that is, the distance between the resolution chart 1 and the zoom lens 2. Hereinafter, specific examples of the optical system including the zoom lens 2 and the front converter 3 will be described in detail.

Example 1
FIG. 2 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22. Here, in describing the lens configuration, the left side in the figure, which is the subject side in a state where the zoom lens 2 is actually used, is referred to as “front”, and the right side in the opposite figure is referred to as “rear”. To do. The other lenses L31 to L42, the aperture stop St, and the parallel plate-shaped optical member PP constitute the zoom lens 2. Note that Sim in the figure indicates an image plane formed by the zoom lens 2 and the front converter 3. The above notation is the same in FIGS. 3 to 11 described later.

Table 1 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment. In the lens data of Table 1, in the column of Si, the surface of the component on the most object side (resolution chart 1 side) is the first and the i-th (i = 1, 2, 3, ...), the Ri column indicates the radius of curvature of the i-th surface, and the Di column indicates the surface spacing on the optical axis Z between the i-th surface and the i + 1-th surface. . In the column of Ndj, the d-line (wavelength: 587.6 nm) of the j-th (j = 1, 2, 3,...) Optical element that sequentially increases toward the image side with the most optical element on the object side as the first. The refractive index with respect to is shown, and the νdj column shows the Abbe number of the j-th optical element with respect to the d-line. The sign of the radius of curvature is positive when convex on the object side and negative when convex on the image side. The lens data includes a resolution chart OBJ, an aperture stop St, and an optical member PP. In the surface number column of the surface corresponding to the aperture stop St, the phrase “aperture stop” is described together with the surface number. The above notation is the same in Tables 3, 5, 7, 9, 11, 13, and 15 described later.

In the lens data in Table 1, the surface number of the aspheric surface is marked with *, and the paraxial curvature radius is shown as the curvature radius of the aspheric surface. Table 2 shows aspheric coefficients which are data relating to these aspheric surfaces.

As the aspheric surface data, the values of the coefficients A _n and K in the aspheric surface expression represented by the following expression (A) are described. More specifically, Zd is the length of a perpendicular line (mm) drawn from a point on the aspheric surface at a height h from the optical axis Z to the tangential plane (plane perpendicular to the optical axis Z) of the apex of the aspheric surface. ).

Zd = C · h ² / {1+ (1− (K + 1) · C ² · h ² ) ^1/2 } + ΣA _n · h ⁿ (A)
(N = an integer greater than 3)
However,
Z: Depth of aspheric surface (mm)
h: Distance from the optical axis to the lens surface (height) (mm)
K: Conic constant C: Paraxial curvature = 1 / R
(R: paraxial radius of curvature)
A _n : n-th aspherical coefficient The above notation is the same in Tables 4, 6, 8, 10, 12, 14 and 16 described later.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₂₀ as aspherical coefficients A _n.

  In the present embodiment, the zoom lens 2 is set at the telephoto end during inspection. That is, the zoom lens 2 is brought into a state of focusing on a subject at infinity. Further, in this embodiment, the focal length f of the zoom lens 2 alone is 63.69 mm, the F value is 5.60, and the angle of view (2ω) is 7.4 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 51.58 mm, the F value is 5.59, and the field angle (2ω) is 9.0 °.

  The spherical aberration, astigmatism, distortion (distortion aberration), and lateral chromatic aberration (chromatic aberration of magnification) in the zoom lens 2 of this embodiment are shown in FIGS. 12A to 12D, respectively. FIGS. 12E to 12H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  Each aberration diagram is based on the d-line having a wavelength of 587.6 nm, but the spherical aberration diagram also shows aberrations relating to the wavelength 460.0 nm and the wavelength 615.0 nm, and the magnification chromatic aberration diagram shows the wavelength 460.0 nm and the wavelength 615. Aberrations related to 0 nm are shown. In the astigmatism diagram, the sagittal direction is indicated by a solid line, and the tangential direction is indicated by a broken line. Fno. Of spherical aberration diagram. Means F value, and ω in other aberration diagrams means half angle of view. The above notation is the same in FIGS. 13 to 19 described later.

  Table 17 shown later collectively shows the angular magnification γ of the front converter 3 and the above-described value of 1000 / fb in the first embodiment and the second to eighth embodiments described later. As shown here, in this embodiment, the angular magnification γ is less than 1, and the condition of the above-described expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In Table 17, for reference, the above-mentioned JP-A Nos. 2006-119346, 2006-39102, 2006-84811, 2007-178826, and JP-A-63-100404 are described. The numerical values in the configuration described in the publication are also described.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν1p of the lens L11 that is the positive lens constituting the front group is 42.82 and the Abbe number ν1n of the lens L12 that is the negative lens is 61.13, the condition of the above-described equation (1) is satisfied. Satisfied. This facilitates correction of the chromatic aberration of magnification of the front converter 3.

  On the other hand, since the Abbe number ν2p = 60.67 of the lens L22 which is the positive lens constituting the rear group and the Abbe number ν2n = 39.24 of the lens L21 which is the negative lens, the condition of the above-described equation (2) is satisfied. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

  Further, the radius of curvature of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is ∞, while the radius of curvature of the opposite surface (surface of surface number 6) is = Since -117.52608, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

Example 2
FIG. 3 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22.

Table 3 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment.

In the lens data in Table 3, the aspherical surface has a surface number with an asterisk (*), and the paraxial radius of curvature is shown as the radius of curvature of the aspherical surface. Table 4 shows aspheric coefficients which are data relating to these aspheric surfaces.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₂₀ as aspherical coefficients A _n.

  In the present embodiment, the zoom lens 2 is brought into a state of being focused forward by 5.0 m at the time of inspection. In this embodiment, the focal length f of the zoom lens 2 alone is 63.39 mm, the F value is 5.62, the angle of view (2ω) is 7.4 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 48.27 mm, the F value is 5.61, and the field angle (2ω) is 9.6 °.

  The spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the zoom lens 2 of the present embodiment are shown in FIGS. 13A to 13D, respectively. FIGS. 13E to 13H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  As shown in Table 17 described above, in this embodiment, the angular magnification γ is less than 1, and in particular, the above-described condition of the expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν1p of the lens L11 which is the positive lens constituting the front group is 39.24 and the Abbe number ν1n of the lens L12 which is the negative lens is 60.29, the condition of the above-described equation (1) is satisfied. Satisfied. This facilitates correction of the chromatic aberration of magnification of the front converter 3.

  On the other hand, since the Abbe number ν2p = 60.67 of the lens L22 which is the positive lens constituting the rear group and the Abbe number ν2n = 39.24 of the lens L21 which is the negative lens, the condition of the above-described equation (2) is satisfied. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

  Further, the radius of curvature of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is ∞, while the radius of curvature of the opposite surface (surface of surface number 6) is = Since -117.52608, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

Example 3
FIG. 4 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22.

Table 5 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment.

In the lens data in Table 5, the aspherical surface is marked with * in the surface number, and the paraxial radius of curvature is shown as the radius of curvature of the aspherical surface. Table 6 shows the aspheric coefficients which are data relating to these aspheric surfaces.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₁₀ as aspherical coefficients A _n.

  In this embodiment, the zoom lens 2 is brought into a state of focusing at infinity during the inspection. In this embodiment, the focal length f of only the zoom lens 2 is 87.34 mm, the F value is 5.63, the angle of view (2ω) is 5.0 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 59.46 mm, the F value is 5.62, and the field angle (2ω) is 7.4 °.

  Spherical aberration, astigmatism, distortion (distortion aberration), and lateral chromatic aberration (chromatic aberration of magnification) in only the zoom lens 2 of the present embodiment are shown in FIGS. 14A to 14D, respectively. FIGS. 14E to 14H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  As shown in Table 17 described above, in this embodiment, the angular magnification γ is less than 1, and in particular, the above-described condition of the expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν1p = 40.75 of the lens L11 which is the positive lens constituting the front group and the Abbe number ν1n = 60.64 of the lens L12 which is the negative lens, the condition of the above-described equation (1) is satisfied. Satisfied. This facilitates correction of the chromatic aberration of magnification of the front converter 3.

  On the other hand, the Abbe number ν2p = 61.13 of the lens L22 which is the positive lens constituting the rear group and the Abbe number ν2n = 39.24 of the lens L21 which is the negative lens are satisfied. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

  Further, the radius of curvature of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is ∞, while the radius of curvature of the opposite surface (surface of surface number 6) is = Since the value is −137.87199, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

Example 4
FIG. 5 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22.

Table 7 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment.

In the lens data in Table 7, the aspherical surface has a surface number with an asterisk (*), and represents the paraxial radius of curvature as the radius of curvature of the aspherical surface. Table 8 shows the aspheric coefficients which are data relating to these aspheric surfaces.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₁₀ as aspherical coefficients A _n.

  In the present embodiment, the zoom lens 2 is brought into a state of being focused forward by 5.0 m at the time of inspection. In this embodiment, the focal length f of only the zoom lens 2 is 87.82 mm, the F value is 5.64, and the angle of view (2ω) is 4.9 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 54.96 mm, the F value is 5.65, and the field angle (2ω) is 7.9 °.

  Spherical aberration, astigmatism, distortion (distortion aberration), and lateral chromatic aberration (chromatic aberration of magnification) in only the zoom lens 2 of the present embodiment are shown in FIGS. 15 (A) to 15 (D), respectively. FIGS. 15E to 15H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  As shown in Table 17 described above, in this embodiment, the angular magnification γ is less than 1, and in particular, the above-described condition of the expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν1p of the lens L11 which is the positive lens constituting the front group is 39.24 and the Abbe number ν1n of the lens L12 which is the negative lens is 60.29, the condition of the above-described equation (1) is satisfied. Satisfied. This facilitates correction of the chromatic aberration of magnification of the front converter 3.

  On the other hand, the Abbe number ν2p = 61.13 of the lens L22 which is the positive lens constituting the rear group and the Abbe number ν2n = 39.24 of the lens L21 which is the negative lens are satisfied. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

  Further, the radius of curvature of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is ∞, while the radius of curvature of the opposite surface (surface of surface number 6) is = Since the value is −137.87199, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

Example 5
FIG. 6 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22. FIG. 7 is an enlarged view of the configuration of the zoom lens 2 with the range as ML.

Table 9 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment.

In the lens data in Table 9, the aspherical surface has a surface number with an asterisk (*), and shows the numerical value of the paraxial curvature radius as the curvature radius of the aspherical surface. Table 10 shows the aspheric coefficients which are data relating to these aspheric surfaces.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₂₀ as aspherical coefficients A _n.

  In this embodiment, the zoom lens 2 is brought into a state of focusing at infinity during the inspection. In this embodiment, the focal length f of the zoom lens 2 alone is 121.71 mm, the F value is 5.82, the field angle (2ω) is 3.2 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 49.10 mm, the F value is 5.81, and the field angle (2ω) is 9.4 °.

  Spherical aberration, astigmatism, distortion (distortion aberration), and lateral chromatic aberration (chromatic aberration of magnification) in the zoom lens 2 of the present embodiment are shown in FIGS. 16A to 16D, respectively. FIGS. 16E to 16H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  As shown in Table 17 described above, in this embodiment, the angular magnification γ is less than 1, and in particular, the above-described condition of the expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν2p = 81.54 of the lens L22 which is the positive lens constituting the rear group and the Abbe number ν2n = 46.57 of the lens L21 which is the negative lens, the condition of the above-described equation (2) is satisfied. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

  Further, the radius of curvature of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is ∞, while the radius of curvature of the opposite surface (surface of surface number 6) is = Since it is −84.05283, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

Example 6
FIG. 8 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22. FIG. 9 is an enlarged view of the configuration of the zoom lens 2 with the range as ML.

Table 11 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment.

In the lens data in Table 11, the surface number of the aspherical surface is marked with *, and the numerical value of the paraxial curvature radius is shown as the curvature radius of the aspherical surface. Table 12 shows aspheric coefficients which are data relating to these aspheric surfaces.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₂₀ as aspherical coefficients A _n.

  In this embodiment, the zoom lens 2 is in a state of being focused forward by 7.5 m at the time of inspection. In this embodiment, the focal length f of the zoom lens 2 alone is 139.03 mm, the F value is 5.87, and the angle of view (2ω) is 3.2 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 40.87 mm, the F value is 5.86, and the angle of view (2ω) is 10.8 °.

  The spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the zoom lens 2 of the present embodiment are shown in FIGS. 17A to 17D, respectively. FIGS. 17E to 17H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  As shown in Table 17 described above, in this embodiment, the angular magnification γ is less than 1, and in particular, the above-described condition of the expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν2p = 81.54 of the lens L22 which is the positive lens constituting the rear group and the Abbe number ν2n = 46.57 of the lens L21 which is the negative lens, the condition of the above-described equation (2) is satisfied. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

  Further, the radius of curvature of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is ∞, while the radius of curvature of the opposite surface (surface of surface number 6) is = Since it is −84.05283, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

Example 7
FIG. 10 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22.

Table 13 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment.

In the lens data in Table 13, the surface number of the aspheric surface is marked with *, and the paraxial curvature radius is shown as the curvature radius of the aspheric surface. Table 14 shows aspheric coefficients which are data relating to these aspheric surfaces.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₂₀ as aspherical coefficients A _n.

  In the present embodiment, the zoom lens 2 is brought into a state of being focused forward by 5.0 m at the time of inspection. In this embodiment, the focal length f of the zoom lens 2 alone is 63.39 mm, the F value is 5.62, the angle of view (2ω) is 7.4 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 47.9 mm, the F value is 5.61, and the field angle (2ω) is 9.6 °.

  Spherical aberration, astigmatism, distortion (distortion aberration), and lateral chromatic aberration (chromatic aberration of magnification) in only the zoom lens 2 of the present embodiment are shown in FIGS. 18 (A) to 18 (D), respectively. FIGS. 18E to 18H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  As shown in Table 17 described above, in this embodiment, the angular magnification γ is less than 1, and in particular, the above-described condition of the expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν1p of the lens L11 which is the positive lens constituting the front group is 39.24 and the Abbe number ν1n of the lens L12 which is the negative lens is 60.29, the condition of the above-described equation (1) is satisfied. Satisfied. This facilitates correction of the chromatic aberration of magnification of the front converter 3.

  On the other hand, the Abbe number ν2p = 55.53 of the lens L22 which is the positive lens constituting the rear group and the Abbe number ν2n = 32.10 of the lens L21 which is the negative lens are satisfied. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

  Further, the radius of curvature of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is -866.01906, and the opposite surface (surface of surface number 6) is the other side. Since the radius of curvature = −117.52608, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

Example 8
FIG. 11 shows cross-sectional shapes of the zoom lens 2 and the front converter 3 in the present embodiment. Here, the front converter 3 is shown as CV, and is composed of front group lenses L11 and L12 and rear group lenses L21 and L22.

Table 15 below shows lens data of the zoom lens 2 and the front converter 3 in the present embodiment.

In the lens data of Table 15, the aspherical surface is marked with * in the surface number, and the numerical value of the paraxial radius of curvature is shown as the radius of curvature of the aspherical surface. Table 16 shows the aspheric coefficients which are data relating to these aspheric surfaces.

In the present embodiment, it represents Zd by orders appropriately effectively used up to A ₃ to A ₂₀ as aspherical coefficients A _n.

  In the present embodiment, the zoom lens 2 is brought into a state of being focused forward by 5.0 m at the time of inspection. In this embodiment, the focal length f of the zoom lens 2 alone is 63.39 mm, the F value is 5.62, the angle of view (2ω) is 7.4 °, and the zoom lens 2 and the front converter 3 are combined. The focal length f of the optical system is 48.07 mm, the F value is 5.61, and the field angle (2ω) is 9.6 °.

  Spherical aberration, astigmatism, distortion (distortion aberration), and lateral chromatic aberration (chromatic aberration of magnification) in only the zoom lens 2 of the present embodiment are shown in FIGS. 19A to 19D, respectively. FIGS. 19E to 19H show spherical aberration, astigmatism, distortion (distortion aberration), and chromatic aberration of magnification (chromatic aberration of magnification) in the optical system combined with the converter 3, respectively.

  As shown in Table 17 described above, in this embodiment, the angular magnification γ is less than 1, and in particular, the above-described condition of the expression (3) ′ is also satisfied. As a result, the aberration due to the front converter 3 can be kept small, and the resolution chart 1 can be made sufficiently large to increase the inspection accuracy. Further, as shown in Table 17, the above-mentioned condition of the expression (4) ′ is also satisfied. Thereby, the positional accuracy of the front converter 3 is relaxed.

  In this embodiment, the front group including the lenses L11 and L12 of the front converter 3 has a negative refractive power, and the rear group including the lenses L21 and L22 has a positive refractive power. Thereby, the assembly of the front converter 3 is facilitated, and the influence on the lens performance due to the manufacturing error can be reduced.

  The front group and the rear group are each composed only of a cemented lens. As a result, the occurrence of lens assembly errors in each group is suppressed, so that the influence of the assembly errors on the lens performance can be eliminated.

  Further, since the Abbe number ν1p of the lens L11 which is the positive lens constituting the front group is 39.24 and the Abbe number ν1n of the lens L12 which is the negative lens is 60.29, the condition of the above-described equation (1) is satisfied. Satisfied. This facilitates correction of the chromatic aberration of magnification of the front converter 3.

  On the other hand, the Abbe number ν2p = 64.20 of the lens L22, which is the positive lens constituting the rear group, and the Abbe number ν2n = 34.47 of the lens L21, which is the negative lens. Satisfied. This facilitates correction of chromatic aberration on the axis of the front converter 3.

Further, the curvature radius of the front group side surface (surface of surface number 4) of the cemented lens constituting the rear group is 658.90737, and the curvature of the opposite surface (surface of surface number 6) is the same. Since the radius = -129.55152, the latter surface has a smaller absolute value of the paraxial radius of curvature. Accordingly, as described above, it is possible to easily correct aberrations such as spherical aberration, coma aberration, and astigmatism that need to be corrected while securing the necessary angular magnification γ.

1 Resolution chart 2 Zoom lens (test lens)
3 Front converter 4 Image sensor L11, L12, L21, L22 Front converter lens

Claims (15)

A front converter used for inspecting the zoom lens by forming or projecting a resolution chart with a zoom lens as a subject,
In a front converter disposed between a resolution chart when the image is formed or a projection surface when the projection is performed and a zoom lens set to a state other than the wide-angle end,
In order from the opposite side to the zoom lens, a front group composed of only cemented lenses and having negative refractive power, and a rear group composed of only cemented lenses and having positive refractive power are disposed.
A front converter having an angular magnification of less than 1. When the Abbe number of the positive lens constituting the front group is ν1p, the Abbe number of the negative lens is ν1n, the Abbe number of the positive lens constituting the rear group is ν2p, and the Abbe number of the negative lens is ν2n, The front converter according to claim 1, wherein:
ν1p <ν1n (1)
ν2p> ν2n (2) Compared with the surface of the front group side of the cemented lens constituting the rear group, as claimed in claim 1 or 2, wherein the surface on the opposite side has a more absolute value smaller paraxial radius of curvature Front converter. The following equation is satisfied, where γ is the angular magnification and fb is the back focus when the distance from the resolution chart when the image is formed to the front converter is 1000 mm. The front converter according to any one of 1 to 3 .
0.1 <γ <0.9 (3)
−0.25 <1000 / fb (4) The front converter according to claim 4, wherein values of the angular magnification γ and the back focus fb satisfy the following expression.
0.2 <γ <0.9 (3) ′
−0.25 <1000 / fb <0.2 (4) ′ In a zoom lens inspection method for inspecting the zoom lens by forming or projecting a resolution chart with a zoom lens as a subject,
A projection surface in the case where the resolution chart, or the projection when the imaging is performed is made, between the set zoom lens to a state other than the wide-angle end, placing the front converter with less than one angular magnification ,
As the front converter, in order from the opposite side to the zoom lens, a front group including only a cemented lens and having negative refractive power, and a rear group including only a cemented lens and having positive refractive power are disposed. inspection method of the zoom lens according to claim Rukoto using that is. As the front converter, the Abbe number of the positive lens constituting the front group is ν1p, the Abbe number of the negative lens is ν1n, the Abbe number of the positive lens constituting the rear group is ν2p, and the Abbe number of the negative lens is ν2n. 7. A method for inspecting a zoom lens according to claim 6, wherein a lens satisfying the following formula is used.
ν1p <ν1n (1)
ν2p> ν2n (2) Examples front converter, as compared with the surface of the front group side of the cemented lens constituting the rear group, claims, characterized in that used as the surface of the opposite side has a more absolute value smaller paraxial radius of curvature 6 Or a zoom lens inspection method according to 7 ; As the front converter, one that satisfies the following formula is used, where γ is the angular magnification and fb is the back focus when the distance from the resolution chart when the image is formed to the front converter is 1000 mm. inspection method of the zoom lens according to claim 6 8 any one of claims from, characterized in.
0.1 <γ <0.9 (3)
−0.25 <1000 / fb (4) The zoom lens inspection method according to claim 9, wherein the values of the angular magnification γ and the back focus fb satisfy the following expression.
0.2 <γ <0.9 (3) ′
−0.25 <1000 / fb <0.2 (4) ′ In a zoom lens inspection apparatus in which a resolution chart is formed or projected by the zoom lens in order to use the zoom lens for inspection,
A front converter having an angular magnification of less than 1 is disposed between a resolution chart when the image is formed or a projection surface when the projection is performed and a zoom lens set to a state other than the wide-angle end. ,
As the front converter, in order from the opposite side to the zoom lens, a front group including only a cemented lens and having negative refractive power, and a rear group including only a cemented lens and having positive refractive power are disposed. What is used is a zoom lens inspection device. As the front converter, the Abbe number of the positive lens constituting the front group is ν1p, the Abbe number of the negative lens is ν1n, the Abbe number of the positive lens constituting the rear group is ν2p, and the Abbe number of the negative lens is ν2n. 12. The zoom lens inspection apparatus according to claim 11, wherein a lens satisfying the following formula is used.
ν1p <ν1n (1)
ν2p> ν2n (2) The front converter is characterized in that the opposite surface has a smaller absolute value of the paraxial curvature radius than the front lens surface of the cemented lens constituting the rear lens group. The zoom lens inspection apparatus according to claim 11 or 12 . As the front converter, one satisfying the following formula is used, where γ is the angular magnification and fb is the back focus when the distance from the resolving power chart when the image is formed to the front converter is 1000 mm. and that it inspection apparatus of the zoom lens according to claim 11 to 13, wherein any one of said.
0.1 <γ <0.9 (3)
−0.25 <1000 / fb (4) 15. The zoom lens inspection apparatus according to claim 14, wherein values of the angular magnification γ and the back focus fb satisfy the following expression.
0.2 <γ <0.9 (3) ′
−0.25 <1000 / fb <0.2 (4) ′

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