High-Dynamic Pixel Array Detectors

• High-dynamic pixel array detectors (HDR-PADs) are advanced imaging sensors that simultaneously capture low and high signal intensities using adaptive gain and dynamic charge removal.
• They achieve an exceptional per-pixel dynamic range through hybrid architectures combining charge integration, in-pixel digital counters, and rapid analog-to-digital conversion.
• HDR-PADs are critical for high-flux experiments such as XFEL imaging, synchrotron diffraction, and ultrafast STEM, enabling quantitative measurements under extreme conditions.

High-dynamic pixel array detectors (HDR-PADs) constitute a class of imaging sensors characterized by their ability to simultaneously resolve extremely small and exceedingly large signals at each pixel, over timeframes compatible with state-of-the-art photon, X-ray, and electron sources. These detectors are critical in synchrotron, XFEL, and STEM environments, achieving dynamic ranges per pixel from 10³ to beyond 10⁸ within a single frame, while maintaining single-particle (photon or electron) sensitivity and minimal dead time. Architectural advances—including adaptive gain, in-pixel charge removal, digital counters, and deep in-pixel analog or digital storage—have enabled this capacity across diverse application regimes and sensor materials.

1. Principles and Architectures of High-Dynamic Pixel Array Detectors

HDR-PADs typically employ hybrid architectures, with a separate sensor diode layer (Si, CdTe, etc.) bump-bonded pixel-by-pixel to a custom CMOS readout ASIC. The key technical strategies for achieving high dynamic range are:

• Charge Integration with Adaptive Gain: Incoming charge is integrated on a selectable or automatically-switched feedback capacitance. Adaptive gain allows optimization for low signals (single-photon sensitivity) and switches to lower gain (higher capacitance) as charge increases, preventing saturation (Trunk et al., 2019, Tate et al., 2015, Becker et al., 2016).
• Dynamic Charge Removal: At the pixel level, a comparator detects when the integrator approaches its full-well limit, triggering subtraction (removal) of a calibrated amount of charge (ΔQ) without disturbing ongoing integration. Each removal increments an in-pixel digital counter, making the dynamic range limited by the product of counter depth and ΔQ, plus the analog residue (Weiss et al., 2016, Philipp et al., 2020, Gadkari et al., 2021, Philipp et al., 2021).
• In-Pixel Storage Buffers: For sources delivering rapid pulse bursts (e.g., XFELs), many HDR-PADs embed analog or digital memory cells within each pixel so that hundreds of frames can be captured at MHz rates, and then read out during inter-burst intervals (Koch et al., 2013, Trunk et al., 2019, Becker et al., 2013).
• Direct Digital Readout: At frame end, each pixel’s accumulated digital count (number of charge removals) is combined with its residual analog value—converted by off-chip or in-pixel ADC—providing per-pixel digitization of both high and low signal content (Tate et al., 2015, Gadkari et al., 2021).
• Modular and Tileable Design: Many implementations use ASICs and sensor tiles that are three- or four-side buttable, supporting scalable assembly to megapixel formats with minimal inactive area (Philipp et al., 2020, Gadkari et al., 2021, Philipp et al., 2021).

2. Mathematical Foundation and Performance Metrics

The performance of HDR-PADs is quantified by several metrics, most fundamentally the dynamic range (DR), defined per pixel as:

$DR = \frac{Q_\mathrm{max}}{Q_\mathrm{noise}}$

where $Q_\mathrm{max}$ is the maximum charge measurable before saturation and $Q_\mathrm{noise}$ is the equivalent noise charge (ENC).

Dynamic Range and Full Well:

For charge-removal architectures,

$$Q_\mathrm{max} \approx n_\mathrm{bits}\cdot \Delta Q + \text{analog well}$$

$$DR \approx 2^{n_\mathrm{bits}} \cdot \frac{\Delta Q}{Q_\mathrm{noise}}$$

Typical read noise $Q_\mathrm{noise}$ values are 30–500 electrons rms, enabling DR beyond $10^5$ or more (Weiss et al., 2016, Philipp et al., 2020, Philipp et al., 2021).

Sustained Count Rates and Maximum Flux:

For pixel architectures with high-speed charge removal (e.g., 100 MHz cycles), sustained per-pixel rates exceeding $10^{10}$ photons/s have been demonstrated (Gadkari et al., 2021). The maximum instantaneous flux is limited by charge-removal speed and counter depth.

Linearity:

HDR-PADs maintain linearity of better than 1–5% up to the full-well limit. Charge-removal and appropriately designed gain stages suppress saturation nonlinearity (Becker et al., 2016, Koch et al., 2013, Trunk et al., 2019).

3. Key Implementations: Case Studies

The following table enumerates representative HDR-PAD architectures:

Detector	DR (typical)	Frame Rate	Sensor	Key Mechanisms
MM-PAD-2.1	$>10^8$	10 kHz	Si / CdTe	Charge removal + counters
AGIPD	$10^4$–$10^5$	4.5 MHz	Si	Adaptive gain, deep analog mem.
EMPAD-G2	$1.3\times10^7$	10 kHz	Si	Adaptive gain, charge dump, double-buffered
ePix10k	$10^4$	480 Hz–100 kHz	Si	3-stage auto-ranging gain

Detailed description of selected architectures:

• MM-PAD-2.1 achieves a DR > $10^8$ by integrating up to $2.2\times10^7$ photons (20 keV eq.) per pixel per frame, with a 0.13 ph rms noise floor, and sustained count rates $>3\times10^{10}$ ph/pixel/s (Gadkari et al., 2021).
• AGIPD utilizes a three-stage gain-switching amplifier and 352 in-pixel analog memory cells, capturing full XFEL burst trains at 4.5 MHz with DR $\sim10^4$–$10^5$ (Trunk et al., 2019, Becker et al., 2013).
• EMPAD-G2 employs adaptive gain and rapid charge dump, achieving a dynamic range of $1.2\times10^7$ at 10 kHz with 0.009 e$^-$ noise level (300 keV e$^-$), and continuous imaging for quantitative 4D-STEM (Philipp et al., 2021).
• Hybrid CdTe MM-PADs support high-energy imaging (up to 200 keV) with per-frame DR $>4\times10^7$, leveraging the high QE of thick CdTe (Becker et al., 2016, Philipp et al., 2020).

4. Sensor Materials, Readout Electronics, and Trade-Offs

Sensor Layer:

• Silicon (Si): Dominant in soft- to mid-energy X-ray and electron detectors; excellent intrinsic noise, but limited at $>30$ keV due to falling QE (Gadkari et al., 2021, Koch et al., 2013).
• CdTe: Selected where $E>20$ keV and high stopping power are required; offers $>$90% QE up to $\sim80$ keV, and useful QE up to $>$100 keV, but can exhibit polarization at high doses and must be carefully biased and cooled (Becker et al., 2016, Philipp et al., 2020, Gadkari et al., 2021).

Readout Electronics:

• Adaptive Gain and Dynamic Range: Per-pixel gain switching (multiple feedback capacitors or parallel amplifiers), often triggered by fast in-pixel discriminators to route large signals into lower-gain circuits (Trunk et al., 2019, Koch et al., 2013, Blaj et al., 2019).
• In-Pixel Digital Counters: For architectures employing charge removal, counter depth ($n$ bits, typically $n=16$–18) directly sets maximal measurable charge per frame (Weiss et al., 2016, Tate et al., 2015).
• Analog and Digital Pipeline: Analog storage cells or dual-buffered integrators enable deadtime-free detection in burst operation or continuous read-while-acquire mode (e.g., EMPAD-G2, MM-PAD-2.1) (Philipp et al., 2021, Gadkari et al., 2021).

Trade-Offs:

• Smaller pixel sizes enhance spatial resolution and frame rate, but increase input capacitance and noise, and require correspondingly more complex ASIC design to maintain dynamic range.
• Larger full wells (larger C_f, deeper counters) increase DR but may degrade noise or require larger pixels/power.
• Counter depth, charge-removal quanta, and gain-switching thresholds must be optimized for the target application and anticipated flux regime (Becker et al., 2016, Weiss et al., 2016, Gadkari et al., 2021).

5. Applications and Impact

HDR-PADs have enabled or transformed a range of high-brightness experiments:

• XFEL and Synchrotron Imaging: Quantitative measurement of diffraction patterns, direct determination of Bragg peak intensities, and time-resolved crystallography, even under exposure to bursts exceeding $10^{12}$ photons/pulse (Trunk et al., 2019, Koch et al., 2013, Philipp et al., 2020).
• Ultrafast STEM and 4D-STEM: Complete unsaturated diffraction pattern acquisition, quantification of bright field to high-angle scattering, and advanced imaging modalities such as center-of-mass, DPC, and strain mapping (Tate et al., 2015, Philipp et al., 2021).
• High-Energy and Space-Based X-ray Astronomy: Single-photon and bright-source imaging across backgrounds from aW to fW per pixel, with resilience to cosmic-ray hits and high-radiation environments (Baselmans et al., 2016, Gevin et al., 2021).
• Tomography and High-Flux Dosimetry: Simultaneous capture of weak and strong signals without saturation, eliminating the need for beam stops or multiple exposures (Philipp et al., 2020, Becker et al., 2016).

6. Performance Benchmarks and Comparative Summary

The following summarizes salient per-pixel performance parameters from representative detectors:

System	Dynamic Range	Noise Floor	Max Frame Rate	Full Well (8 keV eq., ph)	Single-Photon Sensitivity
MM-PAD-2.1	$1.7\times10^8$	0.13 ph	10 kHz	$2.2\times10^7$ (20 keV eq.)	Yes
AGIPD	$10^4$–$10^5$	240–320 e–	4.5 MHz (burst)	$10^4$ (@12.4 keV)	Yes ($E_\gamma\geq6$ keV)
EMPAD-G2	$1.3\times10^7$	2.6 keV (0.009 e–)	10 kHz	$1.1\times10^5$ @300 keV e–	Yes
ePix10k	$10^4$	67 e– (245 eV)	480 Hz–100 kHz	$1.1\times10^4$ (@8 keV)	Yes
MKID array	$1\times10^5$	$3\times10^{-19}$ W/√Hz	—	$40$ fW (sat. power)	—

All values trace to referenced implementations (Gadkari et al., 2021, Trunk et al., 2019, Philipp et al., 2021, Blaj et al., 2019, Baselmans et al., 2016).

7. Limitations, Challenges, and Prospects

• Counter Size and Clocking: Sufficient counter depth and clocking for charge-removal steps are necessary for optimal DR, but increase area, power, and complexity (Weiss et al., 2016, Gadkari et al., 2021).
• Sensor Effects: High-flux-induced polarization in CdTe sensors, interface charge buildup in Si, and overall radiation hardness remain ongoing concerns for certain application domains, mitigated by carefully chosen bias, annealing, and guard-ring design (Becker et al., 2016, Schwandt et al., 2012, Gevin et al., 2021).
• Calibration and Linearity: Interplay of analog and digital response, gain switching, memory cell droop, and temperature variation require rigorous per-pixel calibration to achieve and preserve linearity (Koch et al., 2013, Trunk et al., 2019).
• Scaling: Tiling of modules into larger arrays must address dead zone minimization, thermomechanical management, and high-throughput readout architectures to preserve effective fill factor and data fidelity (Philipp et al., 2020, Gadkari et al., 2021, Philipp et al., 2021).

HDR-PADs are likely to evolve through further advances in ASIC miniaturization, denser memory architectures, sensor materials optimized for QE and radiation tolerance, and DAQ systems supporting frame rates $>100$ kHz at megapixel scales. Their role in quantitative, high-throughput, and high-dynamic-range imaging is likely to remain central in the next generation of photon and electron science (Gadkari et al., 2021, Philipp et al., 2021).