Microbolometer Beam Profiling

• Microbolometer-based beam profiling is a technique that maps THz radiation using uncooled focal-plane arrays to provide real-time, 2D intensity measurements.
• It integrates THz-sensitive optics, pixel-level thermal responses, and rigorous radiometric calibration to yield accurate spatial beam profiles with high resolution.
• The method facilitates applications in accelerator physics and material evaluation by enabling precise Gaussian beam fitting, divergence estimation, and dynamic range analysis.

Microbolometer-based beam profiling refers to the direct spatially resolved measurement and analysis of terahertz (THz) radiation beams using uncooled microbolometer focal-plane arrays (FPAs). These sensors deliver real-time, 2D intensity maps across a wide THz spectral band, enabling quantitative characterization of broadband THz sources such as laser-wakefield acceleration (LWFA) setups and photoconductive antennas (PCAs). The approach combines pixel-level thermal response with specific THz-sensitive optics, rigorous radiometric and spatial calibration, background correction, and advanced image analysis—including Gaussian beam fitting, divergence estimation, and error quantification. Microbolometer-based systems cover spectral ranges roughly 0.1–20 THz, with spatial resolution typically from tens of microns up to a millimeter depending on array format and imaging geometry. This technique is foundational for performance evaluation of THz sources in accelerator physics, spectroscopy, material characterization, and security imaging (Pak et al., 31 Dec 2025, Zolliker et al., 2021).

1. Microbolometer Sensor Architecture and Performance Metrics

Microbolometer FPAs, such as the FLIR A65 and Swiss Terahertz RIGI S2x, consist of arrays of thermally isolated pixels that change resistance in response to incident THz radiation. Key specifications include pixel pitch (typically 17–25 μm), array size (e.g., 640×512 to 160×120), spectral response (e.g., 5–20 THz for A65 with bandpass filtering, 0.1–18 THz for RIGI S2x), and noise-equivalent power (NEP), setting the minimum resolvable irradiance.

Model	Pixel Size	Array Format	Spectral Range	NEP	Dynamic Range
FLIR A65	17 μm	640×512	5–20 THz	~1×10⁻⁹ W/√Hz	~10⁶:1 (60–68 dB)
RIGI S2x	25 μm	160×120	0.1–18 THz	<1.5 pW/√Hz	~10⁴:1 (14-bit ADC)

Pixel-level THz sensitivity arises from absorption—direct or via coated structures—followed by thermal conduction and readout via resistance changes. Responsivity is linearized in firmware, yielding output proportional to incident power. The NEP determines radiometric precision, with reported frame rates from 9 fps to 100 Hz, allowing both real-time feedback and high-throughput data collection (Pak et al., 31 Dec 2025, Zolliker et al., 2021).

2. Optical and Mechanical Arrangement for Beam Profiling

Optical layouts implement reflective collection and focusing into the microbolometer FPA. For LWFA beam profiling, the configuration uses sequential off-axis parabolic mirrors (OAPs) with large apertures to collect and refocus forward-emitted THz while accommodating the copropagating main laser and electron bunch through a central hole. THz-transparent materials, such as Mylar and HDPE, maintain spectral transmission across the beam path. Lateral magnification is defined by OAP focal lengths ($M = f_2 / f_1$), directly affecting pixel-to-object mapping precision.

In PCA-based systems, a zigzag OAP configuration ensures 1:1 imaging from source to detector, with wire-grid polarizers controlling irradiance and polarization state. For simplified or transmission-mode setups, a single silicon lens can collimate and direct the THz emission onto the sample, with the microbolometer camera (and macro-lens) capturing the transmitted spatial pattern.

Image alignment and plane localization employ heated thermal sources at the object plane, maximizing sharpness and geometric fidelity.

3. Radiometric and Spatial Calibration Procedures

Absolute radiometry leverages blackbody sources and known temperature references propagating through the THz optics, determining a pixel-wise calibration constant $K$ via Planck law convolution with filter and FPA spectral response $S(ν)$:

$$I(ν, x, y) [\text{W}/\text{m}^2/\text{THz}] = K \cdot C(x, y) / [S(ν)\cdot\tau_{opt}(ν)]$$

where $\tau_{opt}(ν)$ is the cumulative transmission of all optical elements. Relative calibration can be achieved by modulating polarizer angles and inserting known absorbers. Flat-field correction (nonuniformity mapping) and dark-frame subtraction are routinely applied. Ruler imaging or translation of known features define the spatial magnification for object-to-pixel scaling. Calibration uncertainty is typically ±10% (blackbody-to-THz extrapolation, transmission measurement) (Pak et al., 31 Dec 2025).

4. Data Acquisition Workflow and Image Correction

Microbolometer-based profiling applies tightly controlled frame integration times (5–10 ms for strong sources; up to hundreds of ms for weak signals), balancing dynamic range ($\sim10^6\!:\!1$ for FLIR A65, $\sim10^4\!:\!1$ for RIGI S2x) against saturation threshold. On-board gain selection, fast analog-to-digital conversion, and USB-3.0 or equivalent system data links support real-time operation.

Preprocessing consists of:

• Dead-pixel replacement (nearest-neighbor smoothing)
• Flat-field and dark-frame correction
• Gaussian or median spatial filtering to suppress high-frequency noise
• Linear rescaling of gray-level extrema for contrast enhancement

Background subtraction uses either "beam-blocked" dark frames or averaged no-beam images for robust removal of ambient and offset signals. Frame stitching (translation-scan cross-correlation) enables mapping of large-area samples. Per-pixel NEP sets the lowest contrast threshold as ∼μW/m² (Zolliker et al., 2021).

5. Quantitative Beam Profile Analysis and Mathematical Formalism

Spatial beam profiles are reconstructed by converting pixel indices to physical coordinates via the calibrated magnification $M$. The raw 2D intensity map $I(x,y)$ is fitted to an elliptical Gaussian:

$$I(x, y) = I_0 \exp\left[-2\left(\frac{(x-x_0)^2}{w_x^2} + \frac{(y-y_0)^2}{w_y^2}\right)\right] + B$$

with $w_x$, $w_y$ as principal-axis radii. The single radial beam radius is given by $w = \sqrt{w_x w_y}$ for elliptical symmetry. Divergence and waist position are determined by repeated measurements at axially separated camera positions $z_1, z_2$, with far-field divergence half-angle computed as

$$\theta = \arctan\left(\frac{w(z_2) - w(z_1)}{z_2-z_1}\right)$$

or analytically from $w(z)$ evolution:

$$w(z) = w_0 \sqrt{1 + \left(\frac{z-z_0}{z_R}\right)^2} \quad z_R = \frac{\pi w_0^2}{\lambda}$$

Beam-radius squared fitting yields $w_0$ and $z_0$. Reported uncertainties are ±1% on $w$ (from pixel scale), ±3% reproducibility (across shots), ±10% radiometric calibration (filter transmission and blackbody extrapolation), and ±5 mrad in divergence for $\theta\sim0.2\,\text{rad}$ (Pak et al., 31 Dec 2025, Zolliker et al., 2021).

6. Limitations, Practical Considerations, and Prospective Developments

Optical designs with central OAP holes obscure peak center intensity; use of annular mirrors or reduced hole size could address this. Microbolometers exhibit reduced sensitivity below ∼5 THz, resulting in underestimated low-frequency emission—complementary pyroelectric or Golay-cell cameras could extend this range. The dynamic range may be extended by HDR acquisition (multiple exposures).

For weak sources (low PCA output, highly attenuating samples), per-pixel irradiance can fall below detection threshold; higher-power sources or cooled microbolometers (lower NETD) are needed to improve SNR. Transmission through ambient air attenuates short-wavelength THz radiation; purging or enclosure reduces this loss. Implementation of bandpass filters enables quasi–multi-spectral profiling.

Automated multi–$z$ scanning and real-time fitting offer scalable statistical beam characterization. Analytical extraction of $M^2$ parameters is recommended for full quantitative evaluation but remains rarely implemented in fast-prototyping setups (Pak et al., 31 Dec 2025, Zolliker et al., 2021).

7. Applications and Impact in Contemporary THz Science

Microbolometer-based THz profiling enables absolute, single-shot, spatially resolved characterization of sub-picosecond, broadband pulses as found in high-field LWFA sources and PCAs. The technique underlies benchmarking of divergence (∼0.2 rad for 100-TW LWFA (Pak et al., 31 Dec 2025)), beam waist (down to 0.65 mm FWHM (Zolliker et al., 2021)), spatial uniformity, and output power. The method supports laser-plasma accelerator development, security screening, material imaging, and non-destructive evaluation. The real-time visual feedback (up to 100 Hz) is instrumental for dynamic source alignment and rapid diagnostic scanning. Integration with bandpass filtering and multi–$z$ evaluation provides direct access to source performance metrics, opening paths to routine, cost-effective multi-spectral THz imaging. A plausible implication is that further advances in cooled microbolometer arrays and reflective relay design will enable profiling of increasingly weak or spectrally extended THz sources in accelerator and sensing technologies.