J. Eur. Opt. Society-Rapid Publ. 22, 9( 2026) 89
extends over a very large volume of 200 mm 200 mm 25 mm. The entire stage is located in a large aluminum chamber to reduce influences such as air turbulence and temperature fluctuations. To quantify the performance of the writing head, a fringe observation system was implemented and placed instead of the substrate.
3.1 Writing head
Figure 4 shows the design of the writing head. There are basically two beam paths generated by two different laser sources, which are described in detail below. The laser source of the writing beam is a TOPTICA BlueMode laser head with a wavelength of 405 nm. The collimated beam with a diameter of 1.8 mm and a Gaussian intensity distribution( TEM 00) is divided by PBS2 into a horizontally polarized and a vertically polarized beam. Subsequently, the two beams are reflected by the mirrors M1 and M2 and interfere in the substrate plane. The half waveplate HWP2 rotates the linear polarization angle of the right beam, so the polarization states of both beams offer the best contrast of the interference pattern. The tilt of M1 and M2 defines the period p in the substrate plane.
The fringe locking laser is a HeNe laser from SIOS with a wavelength of 632.8 nm and a Gaussian intensity distribution( TEM 00). Thefringelockingbeamwithadiameterof 2 mm is shifted laterally to the writing beam. After reflection at the mirrors the two fringe locking beams are reflected by a double prism retroreflector with an air gap between its short sides. At PBS2 both beams are recombined in the camera path and they interfere at the camera sensor. The achromatic half waveplate HWP1 at 45 ° ensures the equal splitting of both beams at PBS2. The quarter waveplates QWP 1 and 2 generate left and right circular polarization. After reflection at the retroreflector the circular polarization is reversed. By passing the QWPs again, the beams are completely transferred into the camera path with orthogonal polarization. The quarter waveplate QWP 3 in front of the polarization camera transfers the two beams into an orthogonal circular polarization state. This is important for the phase shifting method described in Section 3.2. Since the fringe locking beam has almost the same path geometry as the writing beam, the phase fluctuation approximates well the displacement of the writing spot on the substrate. As the reflection angle of the measuring beam in the retroreflector corresponds to the angle of incidence, the beams always hit the polarization camera at the same angle, regardless of the tilt of the mirrors M1 and M2. Only the lateral position of the interfering beams on the camera chip changes. This means that the tilts of M1 and M2 can be variably adjusted, allowing different fringe periods to be generated. M1 is mounted on a linear piezo actuator. The actuator is a P-753.1CD from Physics Instruments with an integrated capacitive position measuring sensor with a system resolution of 0.1 nm and positioning accuracy of 0.25 nm. The writing head was completely designed and simulated in the Optical CAD software Quaoda [ 22 ]. All mechanical and optical components are mounted on a breadboard with size of 180 230 mm 2( see Fig. 5).
Figure 4. Optical scheme of the writing head. PBS: polarizing beam splitter, HWP: half waveplate, QWP: quarter waveplate, M: mirror.
3.2 Polarization interferometry
The FLIR Blackfly BFS-U3-51S5P-C polarization camera has a polarizer mask in front of the sensor. The mask contains four linear polarizers in the orientation 0 °, 45 °, 90 ° and 135 °, arranged in a repeating pattern throughout the pixel range [ 23 ]. Four polarizer pixels define a superpixel, which contains all the information in a single camera frame to calculate the phase offset between the two beam paths( see Fig. 6). This spatial phase-shifting method is commonly used to measure the surface errors and topography of lenses and mirrors [ 24 ]. Each polarization channel generates a phase-shifted interferogram. This results in the following system of equations:
ðx; yÞ ¼ A þ B cos ½ uðx; yÞŠ; ð7Þ
I 45
I 0 h ðx; yÞ ¼ A þ B cos uðx; yÞþ p i
; ð8Þ
2
I 90 ðx; yÞ ¼A þ B cos ½ uðx; yÞþpŠ ð9Þ
I 135 ðx; yÞ ¼A þ B cos uðx; yÞþ 3
2 p ð10Þ p
where A = I 1 + I 2 and B ¼ 2 ffiffiffiffiffiffiffiffiffiffiffiffi I 1 I 2. Withthissystemof equations the phase difference Du( x, y) for each superpixel x, y can be determined:
uðx; yÞ ¼ arctan I 90 ðx; yÞ�I 0 ðx; yÞ
: ð11Þ I 135 ðx; yÞ�I 45 ðx; yÞ