J. Eur. Opt. Society-Rapid Publ. 21, 19( 2025) 189
Figure 2.( a) Optical setup of the TWI.( b) Example of four camera images with the sub-interferograms of an aspherical specimen created by the four mask positions of the microlens array.( c) Photo of the specimen stage of the TWI showing a specimen and the TWI objective.
multiple secondary object wavefronts that are then collimated and projected by an objective onto the specimen. The different locations of the microlenses in the plane of the microlens array are transformed into differently tilted wavefronts at the specimen. The wavefronts are then reflected at the specimen and then travel back through the objective and collimator and are projected onto the image detector. The reflected wavefronts interfere with the reference wavefront behind the beamsplitter and a rectangular beam stop in the Fourier plane of the imaging optics acts as a spatial frequency filter and therefore avoids subsampling effects on the camera. Depending on the local slope of the surface under test different parts of the differently tilted and reflected wavefronts arrive at the camera leading to several sub-interferograms( patches). In order to avoid overlapping patches and interference of light from neighboring microlenses, a beam stop grid selectively blocks every second row and column of the microlenses, leading with 4 different grid positions to 4 different camera images( Fig. 2b). A small section of the real setup, including the specimen stage, a specimen and the TWI objective is shown in Figure 2c. For further information on the TWI setup and the image formation please refer to [ 11, 13, 17, 19, 21 – 24 ].
2.2 Simulation of specimen position influence on interferograms
For evaluating interferograms in or near the Cat’ s Eye reference position, a virtual specimen of an asphere [ 25 ] is placed in the desired position in the model and the interferograms are simulated. For the specimen positioning in the
Cat’ s Eye position only the central, on-axis microlens of the microlens array is required. In the physical TWI, this configuration can be selected by an iris diaphragm in front of the beam stop grid. Therefore, only rays from the central microlens are simulated. The illumination light gets reflected back by the surface under test, travels through the optical system, is deflected at the beam splitter between the microlens array and the collimator and is cast on the detector by the secondary imaging system. A surface in the Cat’ s Eye position leads to the reflected light having a focal point in the plane of the rectangular beam stop( compare Fig. 2). However, when the surface shifts away from the Cat’ sEye, thereflection is no longer in a singular point and the focal point moves out of the plane of the beam stop. At a certain distance, the beam stop begins to clip the edges of the backreflected light. This leads to an image of the beam stop being visible on the image detector and causes the rectangular shape of the interferograms shown in Figure 3. When the surface is additionally moved in lateral direction, the movement of the focal point causes a lateral shift of the beam stop’ s image. In Figure 3, simulated interferograms of different specimen positions around the Cat’ s Eye reference position are shown.
The interferograms of a specimen sweep along the optical axis( z-axis) are shown in Figure 3a. IntheCat’ sEye position( z = 0 lm), the interferogram is not limited by the beam stop and has a circular shape. The further away the specimen’ s apex is from this position, the more the interferogram is limited by the beam stop aperture, leading to a rectangular shape that gets smaller with larger distances to the Cat’ s Eye position. When the specimen is