J. Eur. Opt. Society-Rapid Publ. 22, 9( 2026) 91
Figure 7. Displacement of M1 by Dx leads to a different optical path. The dashed lines indicate the displacement of the mirror and the resulting path change.
Fringe pattern rotation: ðc rotation Þ d
¼ arctan ðc�1 1 Þ
init
� arctan ðc�1 1 Þ t
: ð17Þ ðc þ1 1 Þ init ðc þ1 1 Þ t
Due to the reflection at the double prism reflector, a lateral displacement with a piezo actuator of M1 by Dx M1 affects a phase shift of the fringe locking beam Du as follows:
u ¼ 2p k ½4 cosðhÞ x M1Š; ð18Þ
where h is the incident angle of the exposure beam and the pre-factor 4 results from the double reflection at the mirror and thus the double passage through the beam path, see Figure 7. The detailed operating principle of the closed-loop system has been reported in [ 25 ].
3.4 Fringe observation system
In order to determine the shift of the interference fringes for calibration and to evaluate the performance of the fringe locking system, a fringe observation system was implemented. A Olympus microscope objective lens( UMPlanFI) with a numerical aperture of 0.95 was placed at the position of the substrate( see Fig. 8a). After the microscope objective, the beams are reflected by a tilted mirror. To image the fringes on the camera chip, a tube lens( TL) with a focal length of f 0
¼ 100 mm was used. The camera used is a Ximea MC124MG-SY-UB with a pixel pitch x pixel = 3.45lm. The integration time was set to 50 ms, corresponding to an effective sampling rate of approximately 20 Hz. Consequently, higher-frequency stage vibrations are temporally averaged by the camera integration and are therefore not directly resolved in the measurements. The result can be seen in Figure 8b. In a next step, the fringe motion is monitored over time. To quantify the fringe displacement in nanometers, the Fourier-transform method [ 19 ] was used. The single steps of the algorithm are visualized in Figure 9. Atfirst, the initial image with 160 160 pixels is 2D-Fourier transformed. The area around the main frequency peak( rectangle marked in red) with 30 30 pixels is shifted to the 2D-Fourier center, i. e. to remove the carrier frequency of the interference pattern. Since only low-frequency changes are examined, all other frequencies are set to zero to minimize noise. With the inverse Fourier-transform, the phase can be calculated from the real part and the imaginary part. Afterwards, the wavefront is unwrapped and a fit with Zernike polynomials within the circular aperture marked in red is applied.
For reference measurements, an initial state is also defined as described in Section 3.3.
The unambiguity range of the fringe movement is half of the fringe period p. One fringe period extends over approximately N pixel = 3 pixels in diagonal in the camera image. With a period of p = 270nm, thelateralmagnification factor M L can calculated by p xpixel ffiffi 2 pffiffi 2
M L ¼ N pixel ¼ 3 3: 45 10�6 m
¼ 54:21; p
270 10 �9 m ð19Þ pffiffi where the factor 2 is given by the diagonal of the pixels. The fringe displacement resolution of this setup was estimated using simple simulations. For this purpose, a stack of fringe images with well-defined displacement was generated. The magnification factor, the pixel pitch and the image size of the observation system were taken into account. The Fourier method was then applied. This leads to a resolution in the sub-nanometer range. The observation system is mounted on the NPMM-200 stage made from Zerodur and Invar. It’ s position is interferometrically controlled.
4 Experimental results
In SBIL systems, the fringe pattern must be stabilized not only in its lateral position, but also in its rotation, i. e. it must be stationary. In this section we first present the tracking of the fringe rotation. We then present the performance of the fringe locking system. All results are compared and evaluated with the fringe observation system described in Section 3.4. The lasers in the writing head were switched on before measurements so that the built-in optics could warm up and thermal expansion during the measurements could be avoided. The data sets are evaluated with the python developer environment ITOM [ 26 ]. The average time delay from the recorded camera image to the piezo controller is 17 ms. With a sampling rate of 60 Hz, the fringe locking system is able to detect and compensate for the drifts of the writing head.
4.1 Fringe rotation tracking
Rotating mirror M2 by angle b around the z-axis, the fringe orientation of the writing spot will change by angle c, as shown in Figure 10. The overlap area of the two exposure beams also changes slightly, but is neglected due to small changes. Due to the Gaussian intensity profile of the writing spot, these non-interfering regions are located at the outer edges of the beam where the intensity is significantly reduced. Consequently, their contribution to the effective exposure dose of the photoresist is minimal and does not lead to a noticeable spreading.
In order to characterize the angular sensitivity of the fringe locking system, M2 is tilted in different steps in a specified time. During this time, the interferograms of the fringe locking signal and the fringe observation system are captured. The Zernike polynomials Z þ1
1 and Z �1
1 are fitted