Fourier transform deflectometry system and method

1. A deflectometry method for the optical inspection of a phase and amplitude object placed in an optical path between a single grating and an imaging system, at a distance h of the grating, wherein the grating forms a contrast-based periodic pattern with the spatial frequencies μ 0 , v 0 in, respectively, orthogonal axes x,y in an image plane, and the imaging system comprises an objective and an imaging sensor comprising a plurality of photosensitive elements, wherein this method comprises the step of:

capturing through the objective, with the imaging sensor, a first image of said pattern distorted by the phase and amplitude object;

and is characterised in that said spatial frequencies μ 0 , v 0 are not higher than the respective Nyquist frequencies of the imaging system on said axes x,y, and this method also comprises the steps of:

calculating a Fourier transform of said first image in a spatial frequency domain;

selecting at least one first— or higher-order spectrum of said Fourier transform and shifting it in said frequency domain so as to substantially place it at a central frequency of said Fourier transform; and

carrying out a reverse Fourier transform of said at least one shifted first- or higher-order spectrum of said Fourier transform so as to obtain a complex function g(x,y)=I(x,y)e iφ(x,y) , wherein I(x,y) is an intensity and φ(x,y) a phase linked to optical deflection angles θ x , θ y in, respectively, the directions of the x and y axes, according to the following formula: φ(x,y)=−2πh(μ 0 tan θ x +V 0 tan θy).

2. The deflectometry method according to claim 1 , wherein several first- and/or higher order spectra of said Fourier transform are selected and shifted in said frequency domain so as to substantially place them at a central frequency of said Fourier transform.

3. The deflectometry method according to claim 1 , further comprising a step of unwrapping said phase.

4. The delfectometry method according to claim 1 , further comprising a step of filtering said intensity below a certain threshold.

5. The deflectometry method according to claim 1 , wherein said steps are carried out with two patterns crossed at an angle with respect to each other.

6. The deflectometry method according to claim 1 , wherein said steps are carried out with the grating in a first position with respect to the object and with the grating in a second position with respect to the object, said first and second positions being offset by a known distance along the optical path.

7. The deflectometry method according to claim 1 , wherein several distorted images of the pattern are captured, with the object at several distances in said optical path with respect to the grating, and additionally comprising the steps of:

combining said several distorted images to obtain a composite image;

calculating a Fourier transform of said composite image in a spatial frequency domain;

selecting at least one first- or higher-order spectrum of said Fourier transform of the composite image and shifting it in said frequency domain so as to substantially place it at a central frequency of said Fourier transform; and

carrying out a reverse Fourier transform of said at least one shifted first- or higher-order spectrum of said Fourier transform of the composite image so as to obtain a complex function g M (x, y)=I M (x,y)e iφ M (x,y) wherein I M (x,y) is an intensity and φ M (x,y) a phase, and I M (x,y) is linked to the contrast level in the composite image.

8. The deflectometry method according to claim 7 , wherein said pattern comprises two crossed sets of parallel fringes with different spatial frequencies μ O,A , v O,A and μ O,B v O,B and said steps of calculating a Fourier transform of the composite image, selecting and shifting said spectrum of said Fourier transform of the composite image, and carrying out a reverse Fourier transform of said shifted spectrum of the Fourier transform of the composite image may be carried out first with a shift close to μ O,A , V O,A , and then with a shift close to μ O,B , V O,B so as to obtain two amplitude maps, respectively I MA (x,y) and I MB (x,y).

9. The deflectometry method according to claim 8 , further comprising a step of combining said two amplitude maps by superposition, addition, and/or multiplication.

10. The deflectometry method according to claim 1 , further comprising the steps of:

capturing a moire image of the distorted pattern, either by aliasing or by superposition with an additional grating at a different distance in the optical axis with respect to the object;

calculating a Fourier transform of said moire image in a spatial frequency domain;

selecting at least one first- or higher-order spectrum of said Fourier transform of the moire image and shifting it in said frequency domain so as to substantially place it at a central frequency of said Fourier transform; and

carrying out a reverse Fourier transform of said at least one shifted first— or higher-order spectrum of said Fourier transform of the moire image so as to obtain a complex function g M (x,y)=I M (x,y)e i φ(x,y) wherein I M (x,y) is an intensity and φ m (x,y) a phase, and I M (x,y) is linked to the contrast level in the moiré image.

11. The deflectometry method according to claim 10 , wherein said steps are carried out with the additional grating in a plurality of different distances in the optical path with respect to the object.

12. The deflectometry method according to claim 7 , wherein said pattern comprises two crossed sets of parallel fringes.

13. The deflectometry method according to claim 1 , wherein said phase and amplitude object is a refractive object, and said first image is an image of said pattern through said refractive object.

14. The deflectometry method according to claim 1 , wherein said phase and amplitude object is a reflective object, and said first image is an image of said pattern reflected by the reflective object.

15. A deflectometry system for the optical inspection of a phase and amplitude object, comprising:

a grating forming a contrast-based periodic pattern with the spatial frequencies μ 0 , V 0 in, respectively, orthogonal axes x,y in an image plane;

an imaging system comprising an objective and an imaging sensor comprising a plurality of photosensitive elements;

a data processing system connected to said imaging sensor; and

means for holding said object in an optical path between said grating and the imaging system, at a distance h of said grating;

this deflectometry system being characterised in that said spatial frequencies μ 0 , v 0 are not higher than the respective Nyquist frequencies of the imaging system on said axes x,y, and in that said data processing system is programmed to:

capture through the objective, with the imaging sensor, a first image of said pattern distorted by the phase and amplitude object;

calculate a Fourier transform, in a spatial frequency domain, of said first image of said pattern distorted by said phase and amplitude object;

select at least one first- or higher-order spectrum of said Fourier transform and shifting it in said frequency domain towards a central frequency of said Fourier transform; and

carry out a reverse Fourier transform of said shifted first-order spectrum of said Fourier transform so as to obtain a complex function g(x,y)=I(x,y)e i φ(x,y) , wherein I(x,y) is an intensity and φ(x,y) a phase linked to optical deflection angles θ x , θ y in, respectively, the directions of the x and y axes, according to the following formula: φ(x,y)=−2πh(μ 0 tan θx+v 0 tan θy).

16. The deflectometry system according to claim 15 , wherein said objective is a telecentric objective.

17. The deflectometry system according to claim 15 , wherein said phase and amplitude object is a reflective object, the deflectometry system further comprising a beam splitter for reflecting said pattern towards the reflective object while transmitting its distorted reflection towards the imaging system.

18. The deflectometry system according to claim 15 , wherein said pattern comprises at least one set of equally-spaced parallel fringes, preferably in the form of a Ronchi pattern.

19. The deflectometry system according to claim 15 , wherein those equally-spaced parallel fringes said spatial frequencies μ 0 ,μ 0 are about ½ the respective Nyquist frequencies of said imaging system on said axes x, y.

20. The deflectometry system according to claim 15 , wherein said pattern comprises two substantially perpendicular sets of equally-spaced parallel fringes.

21. The deflectometry system according to claim 15 , wherein said grating is formed by a contrast pattern, preferably a metal lithographic pattern, printed on a glass plate.

22. The deflectometry system according to claim 15 , wherein said grating is formed by an active matrix screen, such as, for example, an LCD screen.