The algorithm reduces sensitivity to calibration errors.
Segment mirror phasing, a critical step of segment mirror alignment, requires the ability to sense and correct the relative pistons between segments from up to a few hundred microns to a fraction of wavelength in order to bring the mirror system to its full diffraction capability. When sampling the aperture of a telescope, using auto-collimating flats (ACFs) is more economical. The performance of a telescope with a segmented primary mirror strongly depends on how well those primary mirror segments can be phased. One such process to phase primary mirror segments in the axial piston direction is dispersed fringe sensing (DFS). DFS technology can be used to co-phase the ACFs. DFS is essentially a signal fitting and processing operation. It is an elegant method of coarse phasing segmented mirrors. DFS performance accuracy is dependent upon careful calibration of the system as well as other factors such as internal optical alignment, system wavefront errors, and detector quality. Novel improvements to the algorithm have led to substantial enhancements in DFS performance.
The Advanced Dispersed Fringe Sensing (ADFS) Algorithm is designed to reduce the sensitivity to calibration errors by determining the optimal fringe extraction line. Applying an angular extraction line dithering procedure and combining this dithering process with an error function while minimizing the phase term of the fitted signal, defines in essence the ADFS algorithm. The error function, for the time being, is defined as the rms value of the particular signal fitting. ADFS is a unique and significant enhancement to the DFS algorithm, allowing one to reduce requirements upon calibration while obtaining significantly better and more repeatable results than using the simple DFS algorithm. In addition, this enhancement does not require any additional hardware. Moreover, ADFS can overcome hardware related alignment errors such as DFS device positional uncertainties affecting the signal dispersion direction, and still allow one to obtain precise and repeatable piston estimations.
ADFS allows dispersed fringe sensing to be less sensitive to calibration errors. ADFS corrects for piston estimation error terms, which appear in the fitted phase term when processing a DFS signal. The results of the Monte-Carlo type simulations clearly validate the analytical work to prove a correlation exists between calibration-induced piston estimation errors and the algorithm fitted phase.
At the time of this reporting, ADFS is being integrated with the DFS algorithm improvement called Multi-Trace. Multi-Trace is currently the baseline for the dispersed Hartman sensor (DHS) used on-flight for coarse segment alignment of the James Webb Space Telescope (JWST). Because Multi-Trace does not address many degrees of freedom for the calibration process (i.e., rotational, scaling, tangential translation), a hybrid algorithm offers a possible improvement upon these algorithms. ADFS offers marked improvements on the DFS, DHS algorithm, and opens possibilities for broader applications of these processes.