Image-pickup optical system and image pickup apparatus to correct aberration
An image-pickup optical system includes: a first lens provided near an aperture stop and configured to correct aberration; and a second lens arranged between the first lens and an image sensor and configured to collect light, the first lens being a gradient index lens. The degree of freedom of design of a gradient index lens is higher than that of a lens having a constant refractive index, and a gradient index lens thus has a high potential as a device for a lens. Because such a gradient index lens is employed, it is possible to correct aberration without performing expensive processing such as polishing for example. In other words, as a result, costs may be reduced and image-forming properties may not be reduced at the same time.
1. An image-pickup optical system, comprising:
an aperture stop;
a first lens adjacent to the aperture stop,
wherein the first lens is configured to reduce aberration, and
wherein the first lens is a gradient index lens; and
a second lens configured to collect incident light from an object,
wherein a first refractive index distribution N of the first lens is equal to:
(N=N 0 +nr 12 R 2 +nr 14 R 4 +nr 16 ·R 6 +nz 11 Z+nz 12 Z 2 +nz 13 Z 3 ) based on a determination that a ratio of a focal distance f 2 of the second lens to a focal distance f of the image-pickup optical system satisfies the following:
0.9
≤
f
2
f
≤
1.1
where N 0 is a standard refractive index of the gradient index lens, Z is a position of the gradient index lens in an optical-axis direction, R is a position of the gradient index lens in a radius direction of the gradient index lens, nr 1j is a coefficient of a term R j of a refractive index distribution formula, nz 1k is a coefficient of a term Z k of the refractive index distribution formula, j is an even number, and k is an integer number.
2. The image-pickup optical system according to claim 1 , wherein the second lens is a gradient index lens.
3. The image-pickup optical system according to claim 2 , wherein at least one of the first refractive index distribution of the first lens or a second refractive index distribution of the second lens is in an optical-axis direction.
4. The image-pickup optical system according to claim 3 ,
wherein each of the first refractive index distribution and the second refractive index distribution is in the optical-axis direction, and
wherein each of the first lens and the second lens is designed such that a second order differential of the first refractive index distribution of the first lens in the optical-axis direction is positive and a second order differential of the second refractive index distribution of the second lens in the optical-axis direction is negative.
5. The image-pickup optical system according to claim 2 , wherein the second lens is a metamaterial lens.
6. The image-pickup optical system according to claim 5 , wherein the second lens comprises a plurality of metamaterial lenses.
7. The image-pickup optical system according to claim 6 , wherein the plurality of metamaterial lenses of the second lens are arrayed at specific intervals.
8. The image-pickup optical system according to claim 1 , wherein the image-pickup optical system is configured to generate an infrared image of the object.
9. The image-pickup optical system according to claim 1 , wherein the image-pickup optical system is configured to generate a terahertz-wave image of the object.
10. The image-pickup optical system according to claim 1 , wherein the first lens is a gradient index lens.
11. The image-pickup optical system according to claim 1 , further comprising:
an image sensor; and
a sensor window between the second lens and the image sensor,
wherein the aperture stop, the first lens, the second lens, and the sensor window are respectively in an order from the object to the image sensor.
12. The image-pickup optical system according to claim 1 ,
wherein the first lens is a metamaterial lens, and
wherein refractive indexes in a plurality of arbitrary polarization directions of the incident light are constant at an arbitrary point of the metamaterial lens.
13. The image-pickup optical system according to claim 1 , wherein a second order differential of the first refractive index distribution of the first lens in the radius direction increases monotonically.
14. An image pickup apparatus, comprising:
an image-pickup optical system, comprising:
an aperture stop;
a first lens adjacent to the aperture stop,
wherein the first lens is configured to reduce aberration, and
wherein the first lens is a first gradient index lens; and
a second lens configured to collect incident light from an object,
wherein a first refractive index distribution N of the first lens is equal to:
(N=N 0 +nr 12 R 2 +nr 14 R 4 +nr 16 ·R 6 +nz 11 Z+nz 12 Z 2 +nz 13 Z 3 ) based on a determination that a ratio of a focal distance f 2 of the second lens to a focal distance f of the image-pickup optical system satisfies the following:
0.9
≤
f
2
f
≤
1.1
where N 0 is a standard refractive index of the gradient index lens, Z is a position of the gradient index lens in an optical-axis direction, R is a position of the gradient index lens in a radius direction of the gradient index lens, nr 1j is a coefficient of a term R j of a refractive index distribution formula, nz 1k is a coefficient of a term Z k of the refractive index distribution formula, j is an even number, and k is an integer number;
an image detector configured to detect an image generated by the image-pickup optical system; and
an image-signal obtaining unit configured to obtain an imaging signal based on a detection signal from the image detector.
15. The image pickup apparatus according to claim 14 , wherein the second lens is a gradient index lens.
16. The image pickup apparatus according to claim 15 , wherein at least one of the first refractive index distribution of the first lens or a second refractive index distribution of the second lens is in an optical-axis direction.
17. The image pickup apparatus according to claim 16 ,
wherein each of the first refractive index distribution and the second refractive index distribution are in an optical-axis direction, and
wherein each of the first lens and the second lens is designed such that a second order differential of the first refractive index distribution of the first lens in the optical-axis direction is positive and a second order differential of the second refractive index distribution of the second lens in the optical-axis direction is negative.
18. The image pickup apparatus according to claim 15 , wherein the second lens is a metamaterial lens.
19. The image pickup apparatus according to claim 14 , wherein the detected image is an infrared image.
20. The image pickup apparatus according to claim 14 , wherein the detected image is a terahertz-wave image.
21. An image-pickup optical system, comprising:
an aperture stop; and
a first lens adjacent to the aperture stop,
wherein the first lens is configured to reduce aberration,
wherein the first lens is a gradient index lens,
wherein a refractive index distribution N of the first lens is equal to:
N=N 0 +nr 12 R 2 +nr 14 R 4 +nr 16 ·R 6 +nz 11 Z+nz 12 Z 2 +nz 13 Z 3
based on a determination that a focal distance f 2 of a second lens and a focal distance f of the image-pickup optical system satisfies the following:
0.9
≤
f
2
f
≤
1.1
where N 0 is a standard refractive index of the gradient index lens, R is a position of the gradient index lens in a radius direction of the gradient index lens, Z is a position of the gradient index lens in an optical-axis direction, nr 1j is a coefficient of a term R j of a refractive index distribution formula, nz 1k is a coefficient of a term Z k of the refractive index distribution formula, j is an even number, and k is an integer number,
wherein the second lens is configured to collect an incident light from an object, and
wherein the focal distance of the second lens is equal to the focal distance of the image-pickup optical system.