Improved Pixel-wise Calibration for Charge-Integrating Hybrid Pixel Detectors with Performance Validation

TL;DR

This work tackles the challenge of achieving accurate pixel-wise calibration for a $25~\mu$m pitch charge-integrating detector (MÖNCH). It introduces a backside pulsing approach and builds a per-pixel, three-dimensional lookup table (3D LUT) to map ADU signals to energy across the full dynamic range, validated with monochromatic photons and electrons. The 3D LUT achieves negligible energy bias and yields significant energy-resolution improvements (up to about $22\%$ for photons and $21$–$23\%$ for electrons) and a $4\%$ gain in the accuracy of deep-learning-based localization. The method enables rapid calibration (approximately 1 hour) and supports bad-pixel diagnosis and bump-bond yield estimation, with potential applicability to other charge-integrating detectors such as AGIPD and JUNGFRAU.

Abstract

The MÖNCH hybrid pixel detector, with a 25 \textmu m pixel pitch and fast charge-integrating readout, has demonstrated subpixel resolution capabilities for X-ray imaging and deep learning-based electron localization in electron microscopy. Fully exploiting this potential requires extensive calibration to ensure both linearity and uniformity of the pixel response, which is challenging for detectors with a large dynamic range. To overcome the limitations of conventional calibration methods, we developed an accurate and efficient correction method to achieve pixel-wise gain and nonlinearity calibration based on the backside pulsing technique. A three-dimensional lookup table was generated for all pixels across the full dynamic range, mapping the pixel response to a calibrated linear energy scale. Compared with conventional linear calibration, the proposed method yields negligible deviations between the calibrated and nominal energies for photons and electrons. The improvement in energy resolution ranges from 4% to 22% for 15-25 keV photons and from 16% to 23% for 60-200 keV electrons. Deep learning-based electron localization demonstrates a 4% improvement in spatial resolution when using the proposed calibration method. This approach further enables rapid diagnosis of the cause of bad pixels and estimation of bump-bonding yield.

Figures (9)

• Figure 1: Simplified schematic of the pixel electronics in the MÖNCH ASIC, containing a charge-sensitive amplifier, a correlated double sampler (CDS), and configurable gain stages.
• Figure 2: (a) Schematic of the calibration setup. The high voltage from a Keithley 2410 is superimposed on the pulse generated by an Agilent 33250A to bias the backside of the MÖNCH sensor. The combined voltage is applied to the backside of the silicon sensor in the MÖNCH detector, where the signal is amplified by the pixel electronics in the ASIC. (b) Timing structure of the pulse and the MÖNCH detector exposure (not to scale). The pulse is synchronized with the MÖNCH detector exposure with a delay of 10 ns using an external 1 kHz trigger signal. The pulse duration is set to 100 µs, larger than the 50 µs exposure time but shorter than the 600 µs readout period. This ensures that only the rising edge of the pulse is captured by the MÖNCH detector.
• Figure 3: (a) Pixel response at coordinates (100, 100) as a function of equivalent energy, along with linear and spline fits. The offset of the linear fit is constrained to zero. (b) Residuals of the measured pixel response with respect to the linear and spline fits.
• Figure 4: MÖNCH03 $3\times3$ cluster energy spectrum of Sn K$\alpha$ and K$\beta$ fluorescence photons after the 3D LUT calibration, where the energy conversion coefficient was determined using synchrotron monochromatic X-rays. The Sn K$\alpha$ and K$\beta$ lines where the line energies and theoretical relative intensities are taken from XrayBookletSCOFIELD1974121. A Gaussian fit (shown in red) to the Sn K$\beta$ peak yields an energy centroid of 28.484 keV, well aligned with the nominal energy of 28.486 keV XrayBooklet. The good agreement between the Sn K$\beta$ line with the nominal energy indicates the accuracy of the proposed calibration method and demonstrates that laboratory X-ray fluorescence sources can be used to determine the energy conversion coefficient.
• Figure 5: (a) Local gain, i.e., the derivative of the ADU--keV response within a 5 keV window; (b) offset as a function of equivalent energy for different pixels, and averaged over all pixels with error bars representing the standard deviation across pixels. The results are obtained by performing linear fits over a 5 keV sliding window, sampled every 2.5 keV