JP3335901B2 - Optical system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical system in general, and more particularly to an optical system (optical system) that can be used under a wide range of atmospheric pressure conditions.

[0002]

2. Description of the Related Art In general, a plurality of lenses are used for aberration correction in an optical system requiring high imaging performance, such as a photographic lens. The refractive power (reciprocal of the focal length) φ of the single lens constituting the optical system is expressed by the following equation 1.

[0003] _{φ = (n-n a)} (1 / r 1 -1 / r 2) ··· Formula 1

Here, “n” is the refractive index of the lens material,
"N _a" is the refractive index of the atmosphere, "r _1" is the radius of curvature of one refracting surface of the lens, "r _2" is the radius of curvature of the other refractive surface of the lens.

Since the refractive index n _a of the atmosphere changes depending on the atmospheric pressure P, it can be written as the following equation (2).

N _a = n _a (P) Equation 2

Accordingly, the refractive power φ of a single lens is given by the following equation (3).
Has atmospheric pressure dependence.

[0008] φ = φ (P) = ( n-n a (P)) (1 / r 1 -1 / r 2) ··· Formula 3

Next, consider a two-element lens composed of two thin single lenses having refractive powers φ ₁ (P) and φ ₂ (P). FIG. 7 is a diagram showing a configuration of a conventional optical system in which two lenses are combined.

In FIG. 7, 14 is a single lens having a refractive power of φ ₁ (P), 15 is a single lens having a refractive power of ₂ (P), 3 is a detector located at the focal position, and 4 is a single lens. 1
4, a lens barrel for fixing the single lens 15 and the detector 3.

The combined refractive power φ _net (P) of this lens is
It is expressed by the following equation 4. φ _net (P) = φ ₁ (P) + φ ₂ (P) −dφ ₁ (P) φ ₂ (P) Equation 4

Therefore, also in the doublet lens, the refractive power of the constituent single lens changes depending on the atmospheric pressure P, so that the refractive power changes. Even for a set of three or more lenses, the combined refractive power can be calculated by repeating the calculation of the refractive power of the two lenses using Equation 4.

[0013]

In a conventional optical system using a combination of a plurality of lenses as described above, a change in atmospheric pressure causes a change in refractive power.
There is a problem that the focal length and the back focus change.

Therefore, in an optical system of a sensor used in an environment where the atmospheric pressure changes from normal pressure to extremely low pressure, it is necessary to use a sensor having a plurality of optical systems designed according to the atmospheric pressure. There was a problem that cost was large and space efficiency was poor.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide an optical system capable of suppressing changes in focal length and back focus caused by changes in atmospheric pressure and obtaining high imaging performance. With the goal.

[0016]

In the optical system according to the present invention, the atmospheric pressure is P, the refractive power of a lens or a lens group is φ, and the atmospheric pressure dispersion β of the lens or the lens group is β.
Is defined as β = (dφ / dP) / φ, a first lens or lens group having a focal length f ₁ and an atmospheric pressure dispersion ratio β ₁ and a focal length f ₂ and an atmospheric pressure Dispersion rate β ₂
And a second lens or lens group arranged at a distance d in the image space of the first lens or lens group, and a focal length f ₁ , an atmospheric pressure dispersion ratio β ₁ , a focal length f ₂ ,
And between the atmospheric dispersion rate _{β 2, f 1 · β 1} (1 / (d-
f ₁ ) ² ) + β ₂ (1 / f ₂ ) ≒ 0.

Further, the optical system according to the present invention, the first lens or lens group has a positive focal length f _1, the second lens or lens group, having a negative focal length f ₂ Things.

Further, the optical system according to the present invention comprises:
At least one of the first lens or lens group and the second lens or lens group is provided with a diffractive surface.

[0019]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiment 1 An optical system according to Embodiment 1 of the present invention will be described with reference to the drawings. FIG. 1 is a diagram showing a configuration of an optical system according to Embodiment 1 of the present invention. In the drawings, the same reference numerals indicate the same or corresponding parts.

In FIG. 1, 1 and 2 are lenses, 3 is a detector for detecting an image formed by the lenses 1 and 2, and 4 is a lens barrel for fixing the lenses 1, 2 and the detector 3.

This optical system compensates for a change in the combined focal length between the atmosphere and the vacuum by appropriately selecting the materials of the lenses 1 and 2 and the focal length.

Hereinafter, the principle of atmospheric pressure compensation will be described.
The paraxial imaging formula for the lens 1 is expressed by the following formula 5.

1 / s ₁ ′ = 1 / s ₁ + 1 / f ₁ Equation 5

Here, "s ₁ " is the distance of the object point of the lens 1 from the principal point of the lens 1, "s ₁ '" is the distance of the image point of the lens 1 from the principal point of the lens 1, and "f ₁ " is This is the focal length of the lens 1. In FIG. 1, it is assumed that the left side is positive and the right side is negative in FIG.

The distance s ₂ of the object point of the lens 2 from the principal point of the lens 2 is expressed by the following equation 6 by s ₁ ′.

S ₂ = s ₁ ′ −d Equation 6

Where "d" is the principal point of lens 1 and lens 2
This is the distance from the principal point. If s ₁ = ∞, then s ₁ ′ = f ₁ from equation 5 above, so equation 6 becomes equation 7 below.

S ₂ = f ₁ −d Equation 7

When this is differentiated with respect to the atmospheric pressure P, the following equation 8 is obtained.

Ds ₂ / dP = df ₁ / dP = f ₁ · β ₁ Equation 8

Here, “β ₁ ” is a parameter unique to the lens material in which the change in the refractive power of the lens 1 with respect to the change in the atmospheric pressure is standardized by (n−n _a ). Hereinafter, the lens eigenvalues similarly defined as beta ₁ is referred to as atmospheric pressure dispersion rate. The atmospheric pressure dispersion ratio β ₁ is defined by the following equation (9).

Β ₁ = (dn _a / dP) / (n−n _a ) Equation 9

Next, the imaging formula for the lens 2 is expressed by the following equation (10).

1 / s ₂ ′ = 1 / s ₂ + 1 / f ₂ Equation 10

The following equation 11 is obtained by differentiating both sides of the above equation 10 with the atmospheric pressure P.

− (Ds ₂ ′ / dP) · (1 / s ₂ ′ ² ) = − (ds ₂ / dP) · (1 / s ₂ ² ) − (df ₂ / dP) · (1 / f ₂ ² ) (ds ₂ '/ dP) = s ₂ ' ² {f ₁ · β ₁ (1 / s ₂ ² ) + f ₂ · β ₂ (1 / f ₂ ² )} = s ₂ ' ² {f ₁ · β ₁ (1 / (d−f ₁ ) ² ) + β ₂ (1 / f ₂ )} Equation 11

Therefore, the condition for setting the back focus change due to the atmospheric pressure change to 0 can be expressed by the following equation 12, since the right side of equation 11 only needs to be 0.

F ₁ · β ₁ (1 / (d−f ₁ ) ² ) + β ₂ (1 / f ₂ ) ≒ 0 Equation 12

On the other hand, the composite focal length f _net of the lens 1 and the lens 2 is expressed by the following equation (13).

F _net = 1 / (φ ₁ + φ ₂ −dφ ₁ φ ₂ ) Expression 13

Here, “φ ₁ ” and “φ ₂ ” correspond to the lens 1
And the refractive power of the lens 2 and can be expressed by the following equation (14).

Φ ₁ = 1 / f ₁ φ ₂ = 1 / f ₂ Equation 14

As described above, the focal length “f ₁ ” of the lens 1 and the focal length “f” of the lens 2 are set so as to satisfy the conditional expression 12 for the back focus change 0 due to the atmospheric pressure change and the synthetic focal length conditional expression 13. ₂ ”, the distance“ d ”between the principal point of the lens 1 and the principal point of the lens 2, the dispersion ratio of the atmospheric pressure of the lens 1“ β ₁ ”, and the dispersion ratio of the atmospheric pressure of the lens 2“ β ₂ ”. Without this, an optical system that can be used for both vacuum and atmosphere can be obtained.

For example, in the case of a doublet with d = 0, the design is made as follows. At this time, Equations 12 and 13 are
Equations 15 and 16 below are given respectively.

Β ₁ φ ₁ + β ₂ φ ₂ = 0 Equation 15

F _net = 1 / (φ ₁ + φ ₂ ) Equation 16

Therefore, according to equations (15) and (16), lens 1
And the refractive powers “φ ₁ ” and “φ ₂ ” of the lens 2 are calculated by the following equation 1.
What is necessary is just to design so that it may become 7 and Formula 18.

Φ ₁ = {1 / (1−β ₁ / β ₂ )} · (1 / f _net ) Equation 17

Φ ₂ = {1 / (1-β ₂ / β ₁ )} · (1 / f _net ) Equation 18

In the first embodiment, a two-element optical system has been described. However, it is needless to say that the atmospheric pressure of the back focus can be similarly compensated in the case of three or more optical systems.

Embodiment 2 An optical system according to Embodiment 2 of the present invention will be described with reference to the drawings. FIG. 2 is a diagram showing a configuration of an optical system according to Embodiment 2 of the present invention.

In the first embodiment, the refractive power arrangement for realizing Expression 12 or Expression 13 can be realized by making the lens 1 have a positive refractive power and the lens 2 having a negative refractive power. . 2, the same symbols as those in FIG. 1 indicate the same or equivalent parts.

In FIG. 2, reference numeral 5 denotes a lens having a positive refractive power, and reference numeral 6 denotes a lens having a negative refractive power.

The atmospheric pressure dispersion ratio β can be expressed by the following equation 19 by linear approximation at two points of vacuum and atmosphere.

Β = {n _a / (n−n _a )} / △ P Expression 19

Here, “ΔP” is the change in atmospheric pressure between normal pressure and vacuum, and “Δn _a ” is the difference in refractive index between vacuum and normal pressure, which is the following value.

Δn _a = 1.000272 to 1.0000
00 = 2.72 × 10 ⁻⁴

Since ΔP, n _a and Δn _a are constants independent of the material, the atmospheric pressure dispersion β is determined only by the refractive index n of the material.

Here, assuming that the lens material is limited to general glass, the selection range of the refractive index n is “1.44 to 1.44”.
About 1.91 ". In addition, n _a normal pressure (760mm
Hg), 1.000272, in vacuum,
Since it is 1.000000, Δn _a is 1.0002
72-1.000000 = 2.72 × 10 ⁻⁴ .

From the above, the atmospheric pressure dispersion ratio β of a general glass material is in the following range according to Expression 19. 3.0 × 10 ⁻⁴ / ΔP to 6.2 × 10 ⁻⁴ / ΔP

As described above, since the signs of β ₁ and β ₂ are positive in the above equation 12, in order to realize the equation 12, it is sufficient to set f ₁ to be positive and f ₂ to be negative.

Embodiment 3 An optical system according to Embodiment 3 of the present invention will be described with reference to the drawings. FIG. 3 is a diagram showing a configuration of an optical system according to Embodiment 3 of the present invention.

For example, in the above equation (12), when the atmospheric pressure dispersion ratios β ₁ and β ₂ are limited to a general glass material, the refractive power φ ₁ of the lens 7 is expressed by the following equation (17). / F _net is limited to a range obtained by multiplying 2.1 to ∞ (infinity). Further, by determining φ ₁ , the refractive power φ ₂ of the lens 2 is also determined.

From equation (19), since the atmospheric pressure dispersion ratio β is uniquely determined by the refractive index n, it cannot be determined independently of the refractive index like the Abbe number in the achromatic design. What has been described above restricts the degree of freedom in design in the monochromatic aberration correction.

The third embodiment improves the disadvantage of the second embodiment.

In FIG. 3, reference numeral 7 denotes a diffraction / refraction hybrid lens having a diffraction optical system formed on a refraction surface and having a combined refraction power of refraction power by refraction and refraction power by diffraction phenomenon.

Hereinafter, the refractive power of the diffraction / refraction hybrid lens 7 will be described. The refracting power φ _dr of the diffraction / refraction hybrid lens 7 is expressed by the following equation (20).

Φ _dr = φ _r + φ _d Equation 20

Here, “φ _r ” is the refractive power of the refractive lens,
“Φ _d ” is the refractive power of the diffractive lens.

The refractive power of a diffraction lens based on the diffraction phenomenon is independent of the refractive index of the lens material and the atmosphere. Therefore, the atmospheric pressure dispersion ratio of the diffraction / refraction hybrid lens 7 can be made smaller than that of a refraction lens if the lens has the same material and the same refractive power.

Hereinafter, the principle of the generation of refractive power by the diffraction element will be described. FIG. 4 is an explanatory diagram showing how a plane wave incident on a finite aperture is diffracted.

In FIG. 4, reference numeral 8 denotes an incident plane wave, 9 denotes a shielding plate having an opening having a diameter D, 10 denotes a direction in which the plane wave 8 travels, and 11 denotes a direction in which the first-order diffracted light travels.

The plane wave 8 entering the opening of the shielding plate 9 is diffracted at the end of the opening, and the traveling direction changes. The diffracted light, which is the diffracted light, can be represented by the superposition of the 0th, 1st, 2nd to nth order diffracted light, and the traveling direction 11 of the 1st order diffracted light is different from the incident direction 10 of the plane wave 8. Equation 21
Changes by θ represented by.

Θ = λ / πD Expression 21

Hereinafter, the change θ of the traveling direction of the first-order diffracted light with respect to the incident direction of the plane wave is referred to as a diffraction angle. According to Equation 21, the diffraction angle θ changes depending on the size of the diameter D of the opening.

By utilizing the diffraction angle θ described above, a diffraction element having a lens effect can be constructed. FIG. 5 is an explanatory diagram illustrating the principle of a diffraction element having a lens effect. In this figure, the same symbols as those in FIG. 4 indicate the same or corresponding parts, and a description thereof will be omitted.

In FIG. 5, reference numeral 12 denotes a shielding plate in which a large number of annular openings are arranged concentrically, and the width of the annular ring becomes narrower toward the outer ring.

From the above equation (21), the diffraction angle θ increases as the order of the first-order diffracted light from the outer peripheral aperture increases. By appropriately selecting the width of the opening, the light diffracted by each annular opening can be converged at one point. That is, a lens effect can be provided. Assuming that the focal length of this diffraction element is f, the width D (r) of an annular opening having an inner diameter radius of r is given by the following equation (22).
It is represented by

D (r) = λ / (πtan ⁻¹ (r / f)) Expression 22

As can be easily understood, not all the light incident on the diffraction element is condensed at one point, and light other than the first-order diffracted light diffracted toward the inner edge by the annular opening and light that is not diffracted (0 (Diffraction light next), light diffracted outward at the aperture, and light absorbed or reflected by the shielding plate 12 are inefficient.

When a diffraction element as shown in FIG. 6 in which concentric annular grooves (gratings) are formed on the surface of a glass material is used, almost 100% efficiency can be obtained. FIG. 6 is an explanatory diagram showing the principle of a diffraction element using a grating. 6, the same reference numerals as those in FIG. 5 denote the same or corresponding parts, and a description thereof will be omitted.

In FIG. 6, reference numeral 13 denotes a blazed grating lens in which a concentric grating is formed on the surface of a transparent flat plate.

[0083] radius r _m of the rising portion of the m-th grating from the center is expressed by the following equation 23.

R _m = √ (m ² λ ² +2 mfλ) Expression 23

Here, “λ” is a wavelength, and “1 / f = φ” is a refractive power.

The depth L of the grating is represented by the following equation 24, which corresponds to the phase difference Lλ of the incident light.

L = λ / (n−1) Expression 24

Here, “n” is the refractive index of the glass material.

[0089] As can be seen from the above equation 23, the focal length f, is determined from the wavelength lambda, the radius r _m of the ring, does not depend on the refractive index n. Therefore, it is understood that the atmospheric pressure dispersion ratio β of the diffraction lens is 0.

The dispersion of the refractive power of the diffraction / refraction hybrid lens 7 due to the atmospheric pressure is expressed by the following expression 25 from expression 20.

Dφ _dr / dP = dφ _r / dP + dφ _d / dP = dφ _r / dP = −φ _r · β _r Equation 25

Here, “β _r ” is the atmospheric pressure dispersion ratio by the refractive lens of the diffraction / refraction hybrid lens 7.

From the above equation 20, the following equation 26 can be derived.

Φ _r = φ _dr −φ _d Equation 26

Therefore, the above equation (25) becomes the following equation (27).

Dφ _dr / dP = − (φ _dr −φ _d ) · β _r Expression 27

By setting “φ _d ” to an arbitrary value, the atmospheric pressure dispersion of the diffraction / refraction hybrid lens 7 can be made arbitrary.

[0098]

As described above, in the optical system according to the present invention, the atmospheric pressure is P, the refractive power of the lens or lens group is φ, and the atmospheric pressure dispersion β of the lens or lens group is β = ( When defined as dφ / dP) / φ, a first lens or lens group having a focal length f ₁ and an atmospheric pressure dispersion ratio β ₁ , a first lens or lens group having a focal length f ₂ and an atmospheric pressure dispersion ratio β ₂ And a second lens or lens group arranged at a distance d in the image space of the first lens or lens group, and a focal length f ₁ , an atmospheric pressure dispersion ratio β ₁ , a focal length f ₂ , and between the atmospheric dispersion rate _{β 2, f 1 · β 1} (1 / (d
−f ₁ ) ² ) + β ₂ (1 / f ₂ ) ≒ 0, so that the deterioration of the imaging performance due to the change in the atmospheric pressure between the atmosphere and the vacuum is smaller than that of the conventional optical system. The present invention has an effect that it can be used in a device which is small and in which environmental conditions of atmospheric pressure greatly change.

As described above, in the optical system according to the present invention, the first lens or lens group has a positive focal length f ₁ , and the second lens or lens group has a negative focal length. since with distance f _2, an effect that may be used in an apparatus environmental conditions atmospheric pressure is greatly changed.

Further, the optical system according to the present invention provides:
As described above, since at least one of the first lens or lens group and the second lens or lens group is provided with a diffractive surface, an image is formed by a change in atmospheric pressure between the atmosphere and the vacuum. Since the deterioration in performance is smaller than that of the conventional optical system and the atmospheric pressure dispersion of the lens can be set to an arbitrary value, the atmospheric pressure dispersion is set to an arbitrary value independently of the refractive index of the lens material. Therefore, there is an effect that the monochromatic aberration correction design becomes easy.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of an optical system according to Embodiment 1 of the present invention.

FIG. 2 is a diagram showing a configuration of an optical system according to Embodiment 2 of the present invention.

FIG. 3 is a diagram showing a configuration of an optical system according to Embodiment 3 of the present invention.

FIG. 4 is a diagram illustrating how a plane wave incident on a finite aperture is diffracted in the optical system according to Embodiment 3 of the present invention.

FIG. 5 is a diagram for explaining the principle of a diffraction element having a lens effect in an optical system according to a third embodiment of the present invention.

FIG. 6 is a diagram illustrating a principle of a diffraction element using a grating in the optical system according to Embodiment 3 of the present invention.

FIG. 7 is a diagram showing a configuration of a conventional general two-lens lens.

[Explanation of symbols]

1, 2 lenses, 3 detectors, 4 lens barrels, 5 and 6 lenses, 7 diffraction / refraction hybrid lenses.

──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-5-210049 (JP, A) JP-A-61-67036 (JP, A) JP-A-64-51621 (JP, A) JP-A-7-670 183210 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) G02B 9/00 G02B 13/00

Claims (3)

(57) [Claims] When the atmospheric pressure is defined as P, the refractive power of a lens or a lens group is defined as φ, and the atmospheric pressure dispersion ratio β of the lens or the lens group is defined as β = (dφ / dP) / φ, a _first lens or lens group having f ₁ and an atmospheric pressure dispersion ratio β ₁ , and an image of the first lens or lens group having a focal length f ₂ and an atmospheric pressure dispersion ratio β _2. and a second lens or lens group which is arranged at a distance d to the space, the focal length f _1, atmospheric dispersion rate beta _1, during the focal length f _2, and atmospheric pressure dispersion rate beta _2, f ₁ An optical system characterized by having a relationship of β ₁ (1 / (d−f ₁ ) ² ) + β ₂ (1 / f ₂ ) ≒ 0. Wherein said first lens or lens group has a positive focal length f _1, the second lens or lens group, a negative focal length f ₂
The optical system according to claim 1, further comprising: 3. The optical system according to claim 1, wherein a diffractive surface is provided on at least one refracting surface of the first lens or lens group and the second lens or lens group.