Jungfraujoch/docs/FPGA_DATA_ANALYSIS.md

FPGA data analysis

Jungfraujoch FPGA design has incorporated X-ray diffraction image analysis capabilities.

Pixel mask

Pixels can be masked. For each module a 32-bit map of pixels is loaded to FPGA, with non-zero value meaning masked pixels. According to this map, pixels will be assigned a special value (minimum number for signed types and maximum number for non-signed types) and will be excluded from a subsequent analysis.

ADU histogram

Before conversion to photons/energy, an ADU histogram can be calculated for a module. This allows to preserve some signature of unconverted values. This is done on a module-basis and works with bins with 32 ADU width.

For EIGER this can be used as just a histogram procedure.

JUNGFRAU conversion

For JUNGFRAU module images are converted from ADUs to energy value and divided by a given number to keV units. Result of the operation is rounded to integers.

Pixel thresholding

Pixel range can be specified. Pixels below a minimum threshold will be assigned zero. Pixels above a maximum threshold will be assigned saturated pixel value (the largest number for a given bit-width and sign type). This is specifically designed to operate on unsummed frames, so frame-specific parameters (overload/noise) can be handled.

Frame summation

Frames can be summed together (on a per-module basis) in Jungfraujoch, with a limit of 256 frames added together.

Azimuthal integration

To implement azimuthal integration, FPGA is able to sum pixels based on a provided integration map and per-pixel corrections. This way Jungfraujoch implements azimuthal integration with solid angle and polarization corrections. Corrections were implemented according to formulas developed by Jensen et al. (J. Synchr. Rad., 29, 1420-1428, 2022).

Given FPGA limitations, split-pixels cannot be implemented and number of bins is limited as 1024 per detector module. This way 2D azimuthal integration, as needed for example by SAS-TT, cannot be currently implemented with the FPGA card and needs to be done on a CPU. One needs to be careful with per-pixel corrections - their acceptable range is constrained by 16-bit pixed point integer implementation and is tuned for standard SAXS/WAXS range.

Spot finding

Jungfraujoch FPGA implements a built-in spot finder. Spot finder allows to apply the following criteria for finding strong pixels:

1. Resolution criterion - pixels only within a provided resolution range can be considered as strong pixels (calculating resolution map needs to happen on CPU before data collection run).
2. Bad pixels - pixels marked as bad, as well as chip edges and module edges are excluded from spot finding,
3. Overloads - pixels marked as overloads on JUNGFRAU are always included in the strong pixel output, but are excluded for signal-to-noise ratio calculation,
4. Pixel value - pixels above certain threshold value can be marked as strong,
5. Signal-to-noise (SNR) ratio - pixels with SNR above a threshold can be marked as strong,
6. Connected pixels - strong pixels can be discarded if they are "alone", so their 8 directly neighboring pixels are not counted as strong pixels.

While besides bad pixels criterion, all the above are optional (can be turned off), only pixels that fulfill all enabled criteria are selected as strong pixels.

SNR ratio calculation

Signal-to-noise ratio is calculated for a rectangular area. In horizontal direction the area is fixed - line of 1024 pixels is divided into 32 areas each of 32 pixels. This is dictated by the data flow within the FPGA. In vertical direction the area is flexible - it is 15 lines above and below of the given pixel. Given very large box size, approximation are made, for example that N ≈ N-1 in calculating standard deviation.

Region-of-interest (ROI) integration

Each pixel in a module can be assigned to one of 64 ROIs. For each ROIs, sum, sum of squares, max count, and number of valid pixels will be calculated. Jungfraujoch also calculates X and Y values weighted by pixel values, though this feature is not properly tested at the moment and not integrated in downstream analysis.

Pixel statisitics

The following statistics are collected for each module:

• Number of masked pixels
• Number of saturated pixels (excl.masked)
• Number of error pixels (excl. masked)
• Sum of valid pixels in the module
• Minimum value of valid pixels in the module
• Maximum value of valid pixels in the module Valid pixels are not masked, not saturated, not error pixels.

Square root compression

Jungfraujoch FPGA includes lossy compression preserving counting statistic properties of X-ray image, while reducing bit width of an image. Scheme was described in Wakonig et al., J. Appl. Cryst., 53, 574-586, 2020. Pixel value X is replaced with sqrt(N*X), where N is integer constant in range 1 to 16.