Event-Level Voxel Reconstruction in Two-Photon Absorption Scans Using Pixel-Overlap Selection in Timepix3

This paper presents a robust reconstruction framework for event-level voxelisation in two-photon absorption scans using Timepix3, which enables blind, trigger-free timing assignment and eliminates systematic spatial biases by utilizing pixel-overlap selection and charge-weighted cluster timing instead of traditional centroid or earliest-hit methods.

The Gist

Imagine you are trying to take a 3D X-ray of a silicon chip to see how electricity flows inside it. To do this, scientists use a special "laser pen" that shines through the chip, creating tiny sparks of electricity (charge) at a specific point. This is called Two-Photon Absorption (TPA).

The problem is that the silicon chip isn't a smooth surface; it's like a giant grid of millions of tiny buckets (pixels) waiting to catch these sparks. When the laser fires, the spark doesn't just land in one bucket. It splashes, creating a "cluster" of wet buckets around the center.

Now, imagine you are trying to map exactly where the laser was pointing, but you have two big problems:

1. The Splash: You don't know which bucket in the wet cluster is the "center" of the splash.
2. The Clock: You don't have a stopwatch that syncs with the laser. The laser fires randomly, and the buckets just start recording whenever they get wet. You have to figure out the timing just by looking at the data later.

This paper is about a new, smarter way to solve these problems. Here is the breakdown using simple analogies:

1. The Problem with Old Methods

Previously, scientists tried to guess the center of the splash in two ways, and both had flaws:

• The "Average" Method (Centroid): They calculated the average position of all the wet buckets.
  • The Flaw: If the splash is lopsided (more water on the left), the average moves left, even if the laser was actually in the middle. It's like guessing where a person is standing by averaging the location of their left shoe and their right hand—they might be far apart!
• The "First Splash" Method (Earliest Hit): They looked at which bucket got wet first.
  • The Flaw: The first bucket to get wet is often on the very edge of the splash, where the water is thin. It's like hearing a whisper from the edge of a crowd; you might think the sound came from the edge, but the person shouting is actually in the center. This creates a "ghost" image that is shifted away from the truth.

2. The New Solution: "The Heaviest Bucket"

The author, Tianqi Gao, proposes a much simpler and more reliable rule: Look at the bucket that got the most water.

• The Analogy: Imagine a rainstorm hitting a roof made of tiles. The tile directly under the downpour will get the most water. The tiles on the edge get a little splash.
• The Method: Instead of guessing the average or listening for the first splash, the new method simply finds the bucket with the highest charge (the "heaviest" bucket).
• Why it works: Physics tells us that the most charge is always generated right where the laser is focused. By picking the "heaviest" bucket, you are automatically pinpointing the true center of the laser, even if the splash is messy or lopsided.

3. Solving the "No Clock" Problem

Since the laser and the detector aren't synced, the data looks like a chaotic stream of events. How do we know which events happened while the laser was sitting still (a "dwell") versus when it moved to a new spot?

• The Analogy: Imagine you are listening to a drummer who plays a beat, stops, moves to a new spot, and plays again. You don't have a video, just an audio recording.
• The Method: The new framework looks at the gaps between the beats.
  • If the drummer plays rapidly (events are close together in time), they are likely staying in one spot.
  • If there is a long silence (a big gap in time), the drummer must have moved to a new spot.
• The Result: The computer can automatically sort the chaotic data into neat "pages" (voxels) representing different 3D locations inside the chip, without needing an external timer.

4. Why This Matters

This new method is like upgrading from a blurry, shaky photo to a crystal-clear 3D map.

• No Bias: It doesn't get tricked by messy splashes (asymmetric clusters).
• No Extra Gear: It works with "blind" data, meaning you don't need expensive extra equipment to sync the laser and the detector.
• Real-World Use: This helps engineers build better sensors for things like particle colliders, medical imaging, and space telescopes by letting them see exactly how electricity moves inside the silicon, layer by layer.

In a nutshell:
The paper teaches us how to find the exact center of a messy splash in a grid of buckets by simply looking for the wettest bucket, and how to organize a chaotic stream of splashes into a 3D map just by looking at the time gaps between them. It's a smarter, simpler way to see the invisible world inside our chips.

Technical Summary

1. Problem Statement

The paper addresses critical challenges in characterizing silicon detectors using the Two-Photon Absorption Transient Current Technique (TPA-TCT). While TPA-TCT allows for 3D spatial resolution of charge generation, its application to segmented (pixelated) detectors (specifically using Timepix3 readout) introduces two major ambiguities:

1. Cluster Formation: A single laser excitation generates charge carriers that diffuse and drift, activating multiple adjacent pixels within the intrinsic time resolution of the detector. This creates "multi-pixel clusters," making it difficult to associate the signal with a single spatial voxel.
2. Lack of Synchronization: In modern triggerless or asynchronous readout systems (like Timepix3), detector data is not synchronized with the laser pulses. Consequently, there is no external reference to determine the temporal structure of the scan (i.e., which events belong to which laser dwell position) or to assign absolute event timing.

Existing Limitations: Conventional methods often rely on:

• Centroid-based selection: Accepting events only if the cluster center falls within a Region of Interest (ROI). This introduces spatial bias, especially for asymmetric clusters or off-center excitations.
• Earliest-hit timing: Using the Time-of-Arrival (ToA) of the first pixel to timestamp the event. This is sensitive to noise and edge effects, often selecting peripheral pixels rather than the true charge generation center.

2. Methodology

The authors propose a reconstruction framework designed to operate on continuous, unsynchronized data streams without external triggers. The method consists of five key steps:

A. Region of Interest (ROI) Definition

A spatial window $(x_{min}, x_{max}) \times (y_{min}, y_{max})$ is defined in pixel coordinates to encompass the expected TPA excitation area, excluding background noise.

B. Pixel-Overlap Event Selection

Instead of requiring the cluster centroid to be inside the ROI, the framework uses a pixel-overlap criterion. An event is classified as a valid TPA event if at least one constituent pixel lies within the ROI.

• Benefit: This ensures that all relevant clusters (even those partially overlapping the ROI) are retained, preventing the systematic rejection of valid data caused by asymmetric charge sharing.

C. Dwell Reconstruction (Blind Temporal Grouping)

Since there is no external clock, the scan's temporal structure (dwell intervals) is reconstructed directly from the data stream:

• Events are grouped into "dwell intervals" based on their time separation.
• Consecutive events are assigned to the same dwell if the time gap between them ($t_{k+1} - t_k$) is less than a defined threshold ($\Delta t_{gap}$).
• This allows for the blind identification of laser dwell positions and scan geometry.

D. Cluster-Level Timing Estimator

To assign a precise time to a multi-pixel cluster, the authors propose using the Time-Over-Threshold (ToT) of the pixel with the highest deposited charge within the ROI, rather than the earliest ToA.

• Logic: The pixel with the highest ToT corresponds to the location of maximum charge deposition, which is physically closest to the excitation point.
• Contrast: The earliest ToA often occurs at the cluster periphery due to charge diffusion and noise fluctuations, leading to spatial displacement.

E. Voxel Assignment

Each event is mapped to a 3D voxel $(x, y, z)$ based on:

1. The spatial location of the highest-ToT pixel.
2. The reconstructed dwell index (which corresponds to the laser depth/position $z$).
3. The assigned event time ($t_{event}$).

3. Key Contributions

1. Blind Reconstruction Framework: A method to reconstruct the temporal structure of TPA scans (dwell intervals) and assign event timing purely from unsynchronized data streams, eliminating the need for external laser triggers.
2. Pixel-Overlap Selection: A robust event selection criterion that avoids the spatial biases inherent in centroid-based methods, ensuring high efficiency in capturing asymmetric clusters.
3. Highest-ToT Timing Estimator: A novel timing definition that leverages charge magnitude (ToT) rather than arrival time (ToA) to localize the excitation point, providing a stable and physically motivated observable.
4. Data-Driven TPAR Definition: A method to define the "TPA Region" (TPAR) based on accumulated cluster occupancy and highest-ToT frequency, refining the excitation volume without assuming specific scan geometries.

4. Results and Validation

The paper validates the proposed framework through comparative analysis:

• Spatial Bias Analysis: Comparisons between the "Highest-ToT" estimator and the "Earliest-ToA" estimator reveal that the latter is systematically displaced toward the cluster periphery.
• Spatial Separation: The spatial separation ($\Delta r$) between the two estimators is significant and broad, confirming that earliest-hit timing introduces systematic errors in voxel localization.
• Stability: The Highest-ToT pixel distribution is localized and consistent with the expected charge deposition volume, whereas the earliest-ToA distribution is shifted and sensitive to edge effects.
• Robustness: The framework successfully reconstructs dwell structures and assigns voxel timing in continuous data streams, demonstrating applicability to triggerless high-rate environments.

5. Significance

This work provides a general, robust methodology for analyzing TPA data in segmented silicon detectors. Its significance lies in:

• Enabling Triggerless Operation: It allows for high-precision 3D characterization of electric fields and charge transport in silicon sensors using modern, high-speed pixel detectors (like Timepix3) that operate in asynchronous modes.
• Eliminating Systematic Errors: By correcting the spatial and timing biases of traditional centroid/earliest-hit methods, it enables more accurate reconstruction of electric field distributions and charge collection efficiency.
• Scalability: The approach is not limited to specific detector configurations but applies to any system where localized excitations produce spatially extended clusters in unsynchronized readout systems.

In summary, the paper establishes a new standard for voxel-level analysis in TPA-TCT, transforming raw, unsynchronized pixel data into precise 3D maps of detector response properties.