J. Eur. Opt. Society-Rapid Publ. 22, 36( 2026) 361
Figure 8. Left: The NPMM-200 in the experimental lab. For measurements and fabrication processes, the aluminum chamber will be closed. Right: Movable platform and the mounting frame. The laser beams( red marked) are reflected by a mirror corner made of optically smooth, polished Zerodur. Below the platform, three additional interferometer signals are reflected from the rear of a highly polished Zerodur surface.
3.3.1 Fundamental principles
In the detour phase principle, the measured interferogram in one dimension y can be written as
IðyÞ ¼ ay ð Þþby ð Þcos ½ uðyÞþk c xŠ; ð13Þ
where a( y) andb( y) are the non coherent intensity distributions, u( y) denotes the object-induced phase, and k c = 2p / p is the spatial carrier wavenumber determined by the fringe period p.
When the fringes of the writing spot are shifted perpendicular to the fringe orientation by an amount Dy, the interferogram becomes
Iðy � y
Þ ¼ ay� ð yÞ þ by� ð y
Þcos ½ uðy � yÞþk c ðy � yÞŠ: ð14Þ
This transformation introduces an additional phase term / ¼�k c y ¼� 2p p y; ð15Þ
which represents a pure phase offset D / of the complex signal in the Fourier domain. This behaviour is a direct consequence of the detour-phase principle. Any lateral displacement of a periodic structure generates a corresponding linear phase shift in its diffracted orders. The fringes imposed in the carrier-frequency method constitute such a periodic structure with spatial frequency k c. Thus, their lateral displacement does not modify the physical optical path of the writing spot, but instead alters the phase of the spatial frequency component that is isolated during Fourier demodulation. Consequently, the phase offset observed in the carrier-frequency method is determined solely by the fringe period p and the amount of lateral shift Dy.
3.3.2 Data acquisition
An Olympus microscope objective lens( UMPlanFI) with a numerical aperture of 0.95 and an effective focal length of f = 1.8 mm is placed in the focal position of the lithography head instead of the substrate, as shown in Figure 9. After the MO, the beams are reflected by a tilted mirror. To image the fringes on the camera chip, a tube lens( TL) with afocallengthoff 0 = 200 mm is used. Then the lateral magnification factor M L is 111. The camera used is a Ximea MC124MG-SY-UB with a pixel pitch x pixel = 3.45 lm and a total sensor size of 14.2 mm 10.4 mm. An image of the writing spot can be seen in Figure 9. In combination with the NPMM-200, the positioning of FrObSy is measured in six degrees of freedom, which enables high accuracy measurements and positioning.
The fringe motion is monitored over time. The single steps of the data evaluation are visualized in Figure 10. At first, the initial image is cropped to an area with 48 48 pixels( red rectangle). Then the 2D-Fourier transform is applied. The region of interest around the main frequency peak( rectangle marked in red) with 2 2 pixels is shifted to the 2D-Fourier center, i. e. to remove the carrierfrequency of the interference pattern. All other frequencies are set to zero to minimize noise signals. With the inverse Fourier-transform, the phase can be calculated from the real part and the imaginary part. The offset D / of the wavefront is the mean value and represents the fringe movement. At the beginning of the measurement, an initial offset D / is measured and defined as zero. To quantify the movement in nanometers, the period of the fringes has to be determined. Then the fringe movement Dr can be calculated by
r ¼ / p 2p; ð16Þ
where D / is the measured phase with the carrier-frequency method and p is the period of the fringe pattern in nanometers. The determination of p is described in Section 4.2. The data acquisition rate( including camera image acquisition and phase calculation) is about 30 Hz. The integration time of the camera is set to 8 ms. The data sets are evaluated with the python developer environment ITOM [ 13 ].