Detective Quantum Efficiency of the Timepix4 Hybrid Pixel Detector and its Application to Parallel-Beam Diffraction

This paper characterizes the high detective quantum efficiency of the Timepix4 hybrid pixel detector in event-driven mode at 100 kV and 200 kV and demonstrates its capability to capture weak diffraction signals from polycrystalline gold nanoparticles at 200 kV.

The Gist

Imagine you are trying to take a photograph of a very faint, distant star using a camera. If your camera is too slow, the star blurs. If your camera is too noisy, the star gets lost in static. If your camera is inefficient, it misses most of the light, and you have to shine a bright flashlight on the star to see it—which might burn the star out!

This paper is about testing a brand-new, super-fast digital camera designed specifically for looking at the tiniest things in the universe: atoms inside a Transmission Electron Microscope (TEM). This camera is called Timepix4.

Here is the story of how the scientists tested it and what they found, explained simply.

1. The Camera: A Super-Fast Event Recorder

Most old cameras take a "snapshot" of a whole scene at once, like a bucket catching rain. If it rains too hard, the bucket overflows, and you lose data. If it rains too lightly, the bucket stays empty.

The Timepix4 is different. It's an event-driven camera. Imagine instead of a bucket, you have millions of tiny, individual rain gauges (pixels). Each time a single electron (a particle of light) hits a gauge, it instantly clicks and records the exact time and location. It doesn't wait for a "snapshot." It counts every single drop.

Because it counts so fast (billions of times per second), it can handle a heavy "rain" of electrons without overflowing, and it's sensitive enough to catch a single drop in a dry spell. This is crucial for electron microscopy because you often want to look at delicate samples (like proteins) that get destroyed if you shine too much light (electrons) on them.

2. The Test: How Good is the Camera?

The scientists wanted to know two main things about this new camera:

• How much light does it actually catch? (This is called Detective Quantum Efficiency, or DQE).
• How clear is the picture? (This involves measuring noise and blur).

They tested the camera at two different "brightness" levels (acceleration voltages): 100 kV (a bit dimmer) and 200 kV (brighter).

The Results: The "Zero-Frequency" Score

Think of DQE as a grade out of 1.0. A score of 1.0 means the camera catches 100% of the information without adding any noise.

• At the start (low detail): The camera was amazing. It caught about 93% to 96% of the information. This is a huge improvement over older cameras. It means you can see your sample clearly without blasting it with too many electrons.
• At the edge (high detail): As you try to see finer and finer details (higher spatial frequencies), the score drops.
  • At 100 kV, it still did a decent job (about 22% efficiency).
  • At 200 kV, the score dropped to almost zero at the very highest detail.

Why the drop at 200 kV?
Imagine an electron as a bullet. At 100 kV, the bullet is small and hits one target. At 200 kV, the bullet is faster and bigger; when it hits the sensor, it bounces around and hits multiple neighboring pixels at once. This is called "charge sharing." It's like throwing a water balloon that bursts and wets three tiles instead of one. The camera gets confused about exactly where the hit happened, blurring the finest details.

3. The Real-World Test: The Gold Dust Experiment

To prove the camera works in the real world, the scientists took a picture of gold nanoparticles (tiny balls of gold) using a parallel beam of electrons.

• The Challenge: They wanted to see the faintest, most distant rings of the gold pattern. These are like the faint ripples on a pond far from where you threw a stone.
• The Result: Even though the camera struggles with the absolute finest details at high speed, it successfully detected weak signals from the gold particles up to a very high angle (75 mrad).
• The Analogy: It's like being able to hear a whisper in a noisy room. The camera managed to pick up a signal that is 61,500 times weaker than the brightest part of the image. That is a massive dynamic range!

4. Why This Matters

This paper tells us that the Timepix4 is a game-changer for electron microscopy, especially for:

1. Fragile Samples: Because it is so efficient (high DQE at low detail), you don't need to blast delicate biological samples with electrons to see them. You can use a "dimmer switch" and still get a clear picture.
2. Speed: It can take pictures incredibly fast, which is great for watching things move or change in real-time.
3. Weak Signals: It can see very faint diffraction patterns, which helps scientists figure out the atomic structure of new materials.

The Bottom Line

The Timepix4 is like a high-end sports car. It has an incredible engine (speed) and great fuel efficiency (sensitivity). However, if you push it to the absolute limit on a bumpy road (high voltage, high detail), the suspension (charge sharing) makes the ride a bit bumpy. But for 99% of driving conditions—especially when you need to drive carefully over fragile terrain—it is the best car on the market.

The scientists concluded that this detector is perfectly suited for the future of high-resolution, low-damage electron imaging.

Technical Summary

Here is a detailed technical summary of the paper "Detective Quantum Efficiency of the Timepix4 Hybrid Pixel Detector and its Application to Parallel-Beam Diffraction."

1. Problem Statement

The Timepix4 is a state-of-the-art event-driven hybrid pixel detector within the Medipix family, offering high timing resolution (195 ps) suitable for advanced Transmission Electron Microscopy (TEM) applications like 4D-STEM, tomography, and microED. While previous studies have characterized its Modulation Transfer Function (MTF), a comprehensive characterization of its Detective Quantum Efficiency (DQE) and Normalized Noise Power Spectrum (NNPS) in TEM environments was lacking.

Specifically, there was a need to:

• Quantify the detector's performance at standard TEM acceleration voltages (100 kV and 200 kV).
• Understand how charge sharing (where a single electron deposits energy across multiple pixels) affects the MTF, NNPS, and ultimately the DQE, particularly without post-processing clustering algorithms.
• Demonstrate the practical utility of the detector in recording weak diffraction signals in parallel-beam geometry.

2. Methodology

Experimental Setup:

• Detector: Timepix4 ASIC bump-bonded to a 300 µm planar silicon sensor (512 × 448 pixels, 55 µm pitch).
• Microscope: JEOL CryoARM Z300FSC TEM.
• Readout: Merlin T4 system providing 81.92 Gbps optical readout.
• Conditions: Measurements were conducted at 100 kV and 200 kV. The per-pixel detection threshold was set to 1000 electron-hole pairs with a 100 V reverse bias.

Data Acquisition & Processing:

• Flat-field Illumination: Multiple datasets were recorded (4 at 200 kV, 5 at 100 kV) with 50s exposures. Data was saved as event lists (.h5 files).
• Frame Generation: Event lists were converted into 2D frames, each containing a target number of events ($N_{tar} = 5,000,000$) to approximate single-electron statistics.
• Region of Interest: A central 448 × 448 pixel area was selected to avoid edge effects where pixel response is non-uniform.
• MTF Measurement: Measured using a slanted knife-edge method (following Dimova et al.).
• NNPS Calculation:
  • Computed from the variance of frames relative to the mean flat-field image.
  • A Hanning window was applied to reduce spectral leakage.
  • Zero-frequency correction: Since subtracting the mean removes low-frequency components, $NPS(0)$ was calculated separately using image binning (variance of binned frames) to ensure accurate normalization.
• DQE Calculation: Calculated using the standard formula:
  $$DQE(\omega) = DQE(0) \times \frac{MTF^2(\omega)}{NNPS(\omega)}$$
  Where $DQE(0)$ is derived from the mean events per pixel ($d_n$), the average gain factor ($g$), and $NPS(0)$.

Uncertainty Estimation:

• A rigorous error propagation analysis was performed using Monte Carlo methods for MTF and Bootstrap resampling for NPS.
• Sources of uncertainty included beam current measurement, frame-to-frame variance, and MTF fitting parameters.

3. Key Contributions

1. First Comprehensive DQE/NNPS Characterization: Provided the first measured DQE and NNPS curves for the Timepix4 in TEM at both 100 kV and 200 kV in raw data mode (without clustering algorithms).
2. Quantification of Charge Sharing Effects: Demonstrated how charge sharing at higher energies (200 kV) significantly broadens the Point Spread Function (PSF), reducing MTF and altering the noise spectrum compared to 100 kV.
3. Application Demonstration: Validated the detector's capability in parallel-beam diffraction by recording a polycrystalline gold sample, proving its ability to detect weak signals at high scattering angles.
4. Uncertainty Analysis: Provided a detailed statistical framework for estimating uncertainties in DQE measurements for hybrid pixel detectors.

4. Key Results

Performance Metrics (Zero Frequency vs. Nyquist Frequency):

Metric	100 kV	200 kV	Ideal (Theoretical)
DQE (0 Hz)	0.931	0.965	1.000
DQE (Nyquist)	0.221	~0.0004	0.405
MTF (Nyquist)	0.195	0.0046	0.637
NNPS (Nyquist)	0.160	0.053	N/A

• Zero-Frequency DQE: Both voltages show excellent detection efficiency (>93%), with 200 kV slightly higher due to better penetration of the detector's aluminum contact layer.
• Nyquist Frequency DQE:
  • At 100 kV, DQE remains robust at 0.221.
  • At 200 kV, DQE drops drastically to $3.81 \times 10^{-4}$. This is primarily caused by severe charge sharing at higher energies, which lowers the MTF significantly.
• Gain Factor ($g$): The average gain factor (events recorded per incident electron) increased from 2.52 at 100 kV to 4.84 at 200 kV, confirming that higher energy electrons interact with more pixels, creating larger event clusters.

Diffraction Application Results:

• Sample: Polycrystalline gold nanoparticles.
• Resolution: The detector successfully resolved diffraction rings up to a half-angle of 75 mrad (corresponding to a d-spacing of 0.0355 nm).
• Dynamic Range: The effective intensity span ($C_e$) of the radial average profile was calculated to be $6.15 \times 10^4$.
• Signal Detection: Weak diffraction signals beyond 75 mrad were distinguished from noise, demonstrating the detector's utility for high-resolution, low-fluence diffraction.

5. Significance and Implications

• High Zero-Frequency Efficiency: The Timepix4 is confirmed as an excellent detector for low-dose imaging and counting applications where low spatial frequencies dominate, achieving >96% efficiency at 200 kV.
• Limitations at High Frequencies: The sharp drop in DQE at the Nyquist frequency for 200 kV indicates that clustering algorithms (to recombine charge-shared events) are essential for high-resolution imaging or diffraction at high acceleration voltages if raw data is used.
• Future Applications: Despite the raw data limitations at high frequencies, the detector's high frame rate and high zero-frequency DQE make it ideal for:
  • 4D-STEM and Tomography where low fluence is required to minimize radiation damage.
  • MicroED/3DED for protein crystallography.
  • High-resolution Diffraction: The ability to detect weak signals up to 75 mrad suggests strong potential for structural analysis of nanomaterials, provided data processing (like radial averaging or clustering) is applied to mitigate noise.

In conclusion, this work establishes the Timepix4 as a powerful tool for TEM, defining its operational boundaries and highlighting the critical trade-off between high-energy charge sharing and spatial resolution in raw event-driven mode.