90
J. Eur. Opt. Society-Rapid Publ. 22, 9( 2026)
Figure 5.( a) Quadoa model of the SBIL writing head.( b) Photo of the SBIL writing head integrated into the NPMM-200.
Figure 6. Scheme of polarization camera based interferometry. After an image has been captured, the individual polarization channels are sorted and the phases of the superpixels are calculated according to equation( 11). An example measurement is shown on the right. The interference fringes, which are phase-shifted to each other, are clearly visible.
After unwrapping the modulo 2p phase map Du( x, y), the Zernike coefficients are calculated by use of a least-square fit with Zernike polynomials. Accordingly, the phase difference and the tilt in the x- andy- directions can be determined quantitatively. The area-based measuring method can also be used to correctly align the mirrors to each other before the exposure process. The position of the interferogram on the camera sensor provides information about the tilt angle of the two mirrors and therefore about the period of the exposure pattern on the substrate. Furthermore, the overlap of the two beams in the camera image ensures that both mirrors reflect the writing beams onto the substrate at the correct angles. Another important feature is the detection of the fringe orientation, which is defined by the rotation of the mirrors around the z-axis. This characteristic will be investigated in Section 4.
3.3 Closed loop control
Before exposing the photoresist, an initial state“ init” of the fringe locking signal with the desired design parameters of the fringe pattern is defined, i. e. in terms of fringe period, fringe orientation and fringe offset. The measured wavefront W init on the polarization camera can be approximated by a fit with Zernike polynomials with a given circular aperture:
W init ðr; hÞ ¼ X1
X n
n¼0 m¼�1 ðc m n Þ init Z m n ðr; hÞ
¼ðc 0 0 Þ init Z 0
0 þðc �1 1
| fflfflfflfflfflffl { zfflfflfflfflfflffl } Þ init Z �1
1 þðc þ1 1
| fflfflfflfflfflfflfflfflffl { zfflfflfflfflfflfflfflfflffl } Þ init Z þ1
1
: | fflfflfflfflfflfflfflfflffl { zfflfflfflfflfflfflfflfflffl }
Piston Tilt y
Tilt x
The current state at a specific timet can be written as
ð12Þ
W t ðr; hÞ ¼ðc 0
0 Þ t Z 0 0 þðc�1 1 Þ t Z �1
1 þðc þ1 1 Þ t Z þ1
1: ð13Þ
Finally, the deviation d from the initial state at time t can be expressed as
W d ðr; h; tÞ ¼W init ðr; hÞ�W t ðr; hÞ: ð14Þ
whereby the individual deviations can be specified as follow: Fringe Offset:
ðc offset Þ d
¼ðc 0 0 Þ init �ðc0 0 Þ t: ð15Þ
Period drift: |
ðc tilt Þ d ¼ |
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðc �1
1
Þ 2 init þðcþ1
1
Þ 2 init
�
|
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðc �1
1
Þ 2 t þðcþ1
1
Þ 2 t:
|
ð16Þ