Method for high-accuracy wavefront measurement base on grating shearing interferometry

A method for high-accuracy wavefront measurement based on grating shearing interferometry, comprising

• (i) placing an optical imaging system under test (3) in a grating shearing interferometer system,
• positioning an illuminating system (8) on an object space of the optical imaging system under test (3) and an image plane diffraction grating plate (4) on an image space of the optical imaging system under test (3),
• adjusting a first three-dimensional stage (2) to position an object plane diffraction grating plate (1) on an object plane of the optical imaging system under test (3), and adjusting a second three-dimensional stage (5) to position the image plane diffraction grating plate (4) on an image plane of the optical imaging system under test (3);
• (ii) moving the first three-dimensional stage (2) to enable grating line on the object plane diffraction grating plate (1) along a first grating (101) in a y axis direction to move into an object space field-of-view point position of the optical imaging system under test (3),
• moving the second three-dimensional stage (5) to enable a checkerboard grating or a one-dimensional grating in a corresponding direction on the image plane diffraction grating plate (4) to move into the image space field-of-view point position of the imaging system under test (3), wherein an included angle between a diagonal line direction of the checkerboard grating and an x axis or the y axis is 45 degrees,
• obtaining a series of shearing interferograms in the x axis direction by object plane or image plane grating phase-shifting, and
• solving and unwrapping to obtain a shearing phase φx in the x axis direction:
• φ
• x
• =
• unwrap
• ⁡
• (
• arctan
• ⁡
• [
• 2
• ⁢
• a
• 1
• ⁡
• (
• sin
• ⁢
• ⁢
• φ
• 1
• +
• sin
• ⁢
• ⁢
• φ
• -
• 1
• )
• 2
• ⁢
• a
• 1
• ⁡
• (
• cos
• ⁢
• ⁢
• φ
• 1
• +
• cos
• ⁢
• ⁢
• φ
• -
• 1
• )
• ]
• )
• ,
• wherein, at the moment, φ−1=ϕ(x, y)−ϕ(x−Δ, y) represents a shearing phase of 0th-order beam and −1st-order diffracted beam in the x axis direction, and φ1=ϕ(x−Δ, y)−ϕ(x, y) represents a shearing phase of 1st-order diffracted beam and 0th-order beam in the x axis direction, and A is an offset of 1st-order diffracted beam relative to 0th-order beam received on a two-dimensional photoelectric detector (6), and function unwrap (x) represents unwrapping x;
• (iii) moving the first three-dimensional stage (2) to enable a second grating (102) of the grating line on the object plane diffraction grating plate (1) along the x axis direction to move into the object space field-of-view point position of the optical imaging system under test (3);
• obtaining a series of shearing interferograms in the y axis direction by object plane or image plane grating phase-shifting, and
• solving and unwrapping to obtain a shearing phase ϕy in the y axis direction:
• φ
• y
• =
• unwrap
• ⁡
• (
• arctan
• ⁡
• [
• 2
• ⁢
• a
• 1
• ⁡
• (
• sin
• ⁢
• ⁢
• φ
• 1
• +
• sin
• ⁢
• ⁢
• φ
• -
• 1
• )
• 2
• ⁢
• a
• 1
• ⁡
• (
• cos
• ⁢
• ⁢
• φ
• 1
• +
• cos
• ⁢
• ⁢
• φ
• -
• 1
• )
• ]
• )
• ,
• wherein, at the moment, φ−1=ϕ(x, y)−ϕ(x−Δ, y) represents the shearing phase of 0th-order beam and −1st-order diffracted beam in they axis direction, and φ1=ϕ(x+Δ, y)−ϕ(x, y) represents the shearing phase of 1st-order diffracted beam and 0th-order beam in the y axis direction;
• (iv) defining a shear ratio s between +1st-order diffracted beam and 0th-order beam;
• multiplying the shearing phase φx in the x axis direction by 2 to obtain a differential wavefront with a shear ratio of 2s in the x axis direction ΔWx=2φx=ϕ(x+Δ, y)−ϕ(x−Δ, y);
• multiplying the shearing phase φy in the y axis direction by 2 to obtain a differential wavefront with a shear ratio of 2s in the y axis direction ΔWy=2φy=ϕ(x, y+Δ)−ϕ(x, y−Δ);
• and
• obtaining a wavefront aberration W of the optical imaging system under test (3) by using wavefront reconstruction algorithm of shearing interferometer on ΔWx and ΔWy according to a shear ratio of 2s,
• wherein the grating shearing interferometer system comprise the illuminating system (8), the object plane diffraction grating plate (1), the first three-dimensional stage (2), the image plane diffraction grating plate (4), the second three-dimensional stage (5), the two-dimensional photoelectric sensor (6), and a calculation processing unit (7);
• the illuminating system (8) outputs spatially incoherent light;
• the object plane diffraction grating plate (1) is fixed on the first three-dimensional stage (2);
• the image plane diffraction grating plate (4) is fixed on the second three-dimensional stage (5);
• the object plane diffraction grating plate (1) comprises two sets of one-dimensional gratings with vertical grating line directions;
• the image plane diffraction grating plate (4) comprises one set of checkerboard grating or two groups of one-dimensional grating with vertical grating line directions;
• an output end of the two-dimensional photoelectric sensor (6) is connected with the calculation processing unit (7), and
• a xyz coordinate system is established where z axis direction is along the optical axis direction of the grating shearing interferometer, the x axis is along a grating line direction of the second grating (102) on the object plane diffraction grating plate (1), the y axis is along the grating line direction of the first grating (101) on the object plane diffraction grating plate (1), and establishing that movement axes of the first three-dimensional stage (2) and the second three-dimensional stage (5) are respectively the x axis, the y axis, and the z axis.