J. Eur. Opt. Society-Rapid Publ. 21, 12( 2025) 127
( A)
( B)
Figure 4. Alvarez project geometry:( A) Constructed geometry with ø 25.4 mm in CAD program and( B) simulation of the focus variation. ð Z ¼ A x d x 0
Þ 3
3 þ ðx d x0 Þy 2 þ Ex ð d x0 ÞþG ð1Þ
For the specific geometry under consideration, a focal length f 0 = 150 mm, a value d x0 = 3 mm( a shift of �3 mm in relation to each other results in the effect of a flat plane) and the other parameters A = 0.0012 and E = �0.1454 were defined accordingly, G was set to zero. By inserting the parameters into the general equation, the freeform surface is described by the following polynomial equation.
Z ¼ 0:0004 x 3 þ 0:0012 xy 2 þ 0:1454 x ð2Þ
A circular aperture with a diameter of 25.4 mm( 1 inch) with a notch for a defined component alignment was selected as the outer geometry, as shown in Figure 4( A).
Due to the geometric complexity of the freeform surface, a digital process chain for freeform processing had to be developed, which has this mathematical definition of the surface shape to be created as a starting point. The surface was constructed using the optical design software Zemax and exported as a CAD file. This was followed by the data processing of the volumetric body in a CAD program in order to subsequently implement the machining programming( grinding parameters and tool path generation) using CAD / CAM software( PTC Creo). In this step, the determination of the component coordinate system is also an important aspect in order to define the orientation of the geometry in the working area of the grinding machine. Since the samples are produced from a cylindrical workpiece, it is advisable to place the origin of the coordinate system centered in the x-y direction and on the top surface of the component in the z direction, in order to calibrate the sample position to the machine coordinate system using a tactile measuring probe( see Fig. 4( A)). After generation of the CAM data file and application of a post-processor, it was then possible to obtain a file in G-code format that is compatible to the data language of the grinding machine.
3 Material and methods
The investigations of the manufacturing chain combining grinding and PJP were carried out on fused silica( FS).
Due to the well-defined composition, it is the material of choice for adjusting the parameters of processes. In addition to the fact that FS only consists of SiO 2, itslowthermal expansion and low sensitivity to breakage in the presence of thermal gradients during thermal processes makes it beneficial for the PJP process.
In order to assess the form errors with respect to the surface design, a telecentric white light interferometer( TopMap Pro. Surf, Polytec GmbH) offering a measurement field of 23 17 mm 2( stitchable to larger areas) was applied for areal measurement of the ground and ultra-fine ground surfaces. Areal form measurements before and after PJP were performed with the optical non-contact profilometer( CT350S, Cyber Technologies GmbH). The resulting figure error was calculated by matching with the nominal Alvarez design.
Birefringence induced by internal stress was determined using the StrainScope S3 / 180( ilis GmbH). The measured optical path difference( OPD) was normalized to thickness, also to enable the comparison of different samples. Furthermore, the indication of the normalized OPD follows the conventions in the production of precision optics. Investigations on potential bulk material alterations were carried out using Fourier transform infrared( FT-IR) spectroscopy, where the spectra were recorded with a MIR spectrometer( TENSOR II, Bruker Corporation) equipped with a Golden Gate ATR unit and a DTGS detector. The spectra were processed using the OPUS software( version 8.1). X-ray diffraction( XRD) was applied for phase investigations. Here, the 2h / x scan was measured with a diffractometer( ULTIMA IV, Rigaku Holdings Corporation) in out-ofplane geometry with parallel beam optics. A copper anode( Ka k = 0.15406 nm) was used as x-ray source. The diffractometer was equipped with a scintillation detector. The diffractograms were analyzed using the software package PDXL( Rigaku Holdings Corporation).
Microscopic white light interferometers( WLI, NPFLEX, Bruker Corporation and TopMap Micro. View, Polytec GmbH) were used to determine surface waviness and roughness. By using different magnifications( 5, 50), topographical features on different lateral scales were measured. The 5 objective covers a spatial frequency range
of 2.4 10 �3 lm �1 to 7.8 10 �2 lm �1, while the 50 objective is applicable in a range of 2.4 10 �2 lm �1 to