92
J. Eur. Opt. Society-Rapid Publ. 22, 9( 2026)
Figure
8.( a) Draw of the fringe observation system.( b) Captured image of the writing spot fringes.
Figure
9. Scheme of the Fourier-transform method [ 19 ] to determine the fringe movement of the captured image in the fringe observation system.
Figure 10. Fringe rotation c within the writing spot in the substrate plane, due to mirror rotation. The solid circle shows the writing spot with perfect overlapping of the exposure beams. If one of the mirrors M1 or M2 rotates around the z-axis, the exposure beam moves on a circular track. For this reason the spots are not overlapping completely and the fringes change their direction. to obtain the Zernike coefficients c þ1
1 and c �1
1
, as explained in Section 3.3. The angle c is given by equation( 17). Spherical coordinates are used to describe the propagation direction with the wave vector k.
0 1 0 1 k x sinðhÞ cosðbÞ B C B
C kðh; bÞ ¼ @ k y A ¼jkj @ sinðhÞ sinðbÞ A: ð20Þ cosðhÞ k z
The results are shown in Figure 11. Within 60 seconds, five movements of M2 were performed manually. Both measurement systems captured the fringe rotation. The measurement sensitivity depends on the ratio between the incident angles of the two beams h and the mirror rotation b.