Optical system comprising a diffractive optical element, and method of designing the same

• US 20010043397A1
• Filed: 04/25/2001
• Published: 11/22/2001
• Est. Priority Date: 05/13/1998
• Status: Active Grant

• Current Assignee: Olympus Optical Corporation Limited (Olympus Corporation)
• Original Assignee: Olympus Optical Corporation Limited (Olympus Corporation)
• Inventors: Ishii, Tetsuya
• Granted Patent: US 6,330,109 B1
• Time in Patent Office: Days
• US Class Current: 359/571
• CPC Class Codes: G02B 5/1866 Transmission gratings characterised by their structure, e.g. step profile, contours of substrate or grooves, pitch variations, materials G02B5/1809, G02B5/1828, G02B5/1833, G02B5/1838 and G02B5/1847 take precedence

Abstract

The invention relates to a method of easily and quantitatively determining the diffraction efficiency of a relief type diffraction optical element, and provides a method of designing an optical system comprising a diffractive optical element using diffraction efficiency as at least one estimation index. The diffractive optical element is a transmission blaze grating constructed of a relief having a sawtooth shape in section. The transmission blaze grating having a side wall substantially vertical to a grating surface. The estimation index is given by a predetermined mathematical expression including at least a phase difference due to a relief discontinuity and shadow effects thereof. The mathematical expression includes as the shadow effects of said discontinuity at least a light attenuation effect dependent on an angle-of-incidence and a light attenuation effect independent on the angle-of-incidence in a separate manner.

Claims

1. A method of designing an optical system comprising a diffractive optical element using diffraction efficiency as at least one estimation index, characterized in that:

said diffractive optical element is a transmission blaze grating constructed of a relief having a sawtooth shape in section, said transmission blaze grating having a side wall substantially vertical to a grating surface thereof, and

said estimation index is given by a predetermined mathematical expression including at least a phase difference due to a relief discontinuity and shadow effects thereof, said mathematical expression including as the shadow effects of said discontinuity at least a light attenuation effect dependent on an angle-of-incidence and a light attenuation effect independent on said angle-of-incidence in a separate manner.

2. An optical system comprising at least one diffractive optical element on an optical axis thereof, characterized in that:

said diffractive optical element is a transmission blaze grating constructed of a relief having a sawtooth shape in section, said transmission blaze grating having a side wall substantially vertical to a grating surface thereof, and

said optical system comprises said optical axis and at least one entrance surface vertical to a grating groove, wherein an angle θ

_en of an incident light ray with a normal to said grating groove on said entrance surface and a construction of said blaze grating in a region of said grating surface on which said incident light is incident satisfies the following relationship with respect all light rays on said entrance surface upon incidence on said diffractive optical element;

1≧

PSE×

SE>

0.8

where

PSE=|sin π

(m−

φ

)/{π

(m−

φ

)}|²

φ

=h/λ

·

(n_ex cos θ

_ex^(m)−

n_en cos θ

_en)

n_ex sin θ

_ex^(m)=n_en sin θ

_en+mλ

/p

SE={1−

{square root}(SE1²+SE2²)}²

SE1=k₁·

(h/p) tan θ

_ave

SE2=k₂·

λ

/p

θ

_ave=(θ

_en+θ

_ex^(m))/2

k₁=0.85

k₂=0.3·

|h/λ

|^0.35

wherein n_en is a refractive index of an entrance side medium, n_ex is a refractive index of an exit side medium, h is a grating groove depth, p is a grating pitch, m is an order of diffraction at which diffraction efficiency is maximized, θ

_ex^(m) is an angle of an m-order diffracted light ray with the normal to the grating surface, and λ

is a wavelength of light used.

3. The optical system according to

claim 2

, which satisfies the following relationship:

1≧

PSE×

SE>

0.9

4. The optical system according to

claim 2

or

3

, wherein a sign of an angle θ

_en Of incidence of all chief rays on said entrance surface upon incidence on said diffractive optical element with respect to the normal to said grating surface coincides with a sign of said order of diffraction m at which said diffraction efficiency is maximized.

5. The optical system according to

claim 4

, which satisfies the following relationship:

5>

|n_ex−

n_en|>

0.5

6. The optical system according to any one of

claims 2

to

5

, which satisfies the following relationship:

|m|=1

7. The optical system according to any one of

claims 2

to

6

, which is an image formation optical system for forming an image of an object.

8. An optical system, characterized by comprising a transmission blaze grating constructed of a relief having a sawtooth shape in section and satisfying the following relationships:

0.8<

h/h₀|<

16<

|p/h₀|

where h₀=λ

/(n_ex−

n_en), λ

is a wavelength of light used, n_en is a refractive index of an entrance side medium, n_ex is a refractive index of an exit side medium, h is a grating groove depth, and p is a grating pitch.

9. The optical system according to

claim 8

, wherein a sign of an angle θ

_en of incidence of all chief rays on an entrance surface upon incidence on said transmission blaze grating with respect to a normal to a grating surface coincides with a sign of an order of diffraction m at which diffraction efficiency is maximized.