Calibrated Quadrant Photodiode Singleton

• Calibrated Quadrant Photodiode Singleton is a high-precision beam sensor that delivers direct lateral position and angle measurements using a CMM-calibrated mechanical reference.
• It employs a bare InGaAs quadrant photodiode with differential power sensing to achieve micrometer positioning and microradian angular accuracy in interferometric setups.
• Robust calibration procedures and in-lab alignment techniques ensure low noise and high stability, crucial for applications such as the LISA gravitational wave detection experiment.

A Calibrated Quadrant Photodiode Singleton (CQS) is a high-precision beam-position and beam-angle sensor engineered for laboratory interferometric metrology, delivering direct measurements of beam lateral position and pointing vector with micrometer and microradian precision, referenced to a rigid, metrologically calibrated mechanical datum. The CQS was developed for the Three-Backlink-Laboratory (3BL) as part of the construction efforts for the LISA mission, addressing the strict alignment and stability requirements necessary for space-based gravitational wave detection (Bischof et al., 16 Dec 2025).

1. Mechanical and Optical Architecture

The CQS consists of a bare InGaAs quadrant photodiode (GAP1000Q, 1 mm active diameter, factory glass removed) mounted on a Macor spacer, which is in turn pressed and epoxied against the inner face of a brass cuboid. This brass block serves as the primary mechanical reference, featuring three orthogonal, precisely machined faces with positions determined via coordinate-measuring machine (CMM) to within 2 µm. Two orthogonal micrometer screws (100 µm per graduation) enable translation of the block in the X and Y axes relative to the optical bench; the Z position is fixed by the Macor spacer’s known thickness.

Alignment of an incoming Gaussian laser beam (typically 300–600 µm in diameter) to the CQS is achieved by iterative adjustment of the micrometers while monitoring the four quadrant difference signals. Imaging optics are omitted; the beam illuminates all four photodiode quadrants with high-contrast Gaussian overlap, supporting high linearity in differential readout.

2. Operating Principles and Readout Model

The CQS utilizes the standard differential power sensing (DPS) protocol for quadrant photodiodes. Defining quadrant currents as $I_1$ (upper-left), $I_2$ (upper-right), $I_3$ (lower-right), and $I_4$ (lower-left), the total photocurrent $I_\text{tot}$ and differential signals are calculated as: $I_\text{tot} = I_1 + I_2 + I_3 + I_4$

$\varepsilon_x = (I_2 + I_3) - (I_1 + I_4)$

$\varepsilon_y = (I_1 + I_2) - (I_4 + I_3)$

Normalized difference signals,

$$X_n = \frac{\varepsilon_x}{I_\text{tot}},\quad Y_n = \frac{\varepsilon_y}{I_\text{tot}},$$

exhibit linearity to first order in small beam displacements, yielding

$\Delta x = k_x X_n,\quad \Delta y = k_y Y_n,$

with slope factors $k_x$, $k_y$ (in mm) determined by calibration. Beam angle ($\theta_x$, $\theta_y$) is calculated by two-point differencing: two CQS units separated by a lever arm $L_z$ along the beam axis produce position readings $\Delta x_1$, $\Delta x_2$, with the tilt given by

$$\theta_x = \frac{\Delta x_2 - \Delta x_1}{L_z},\quad \theta_y = \frac{\Delta y_2 - \Delta y_1}{L_z}.$$

3. Calibration Methodology

CQS calibration encompasses geometric referencing, transduction scaling, and laboratory alignment:

• Step 1: CMM-based geometry determination. The bare brass block (without photodiode) is measured in the CMM, establishing the positions of its three datum planes to ±2 µm. After reassembly with the QPD, the combined unit’s faces are remeasured, and the photodiode center ($x_0$, $y_0$, $z_0$) is inferred.
• Step 2: Photocurrent-to-position slope determination. A two-axis translation stage moves a well-collimated test beam in precise increments across the active area. For each step (e.g., ±500 µm in 100 µm increments), the corresponding normalized signals ($X_n$, $Y_n$) are recorded. Slope factors $k_x$, $k_y$ (typically ≈1 mm) are extracted from linear fits of $\Delta x_\text{meas}$ versus $X_n$ ($\Delta y_\text{meas}$ versus $Y_n$).
• Step 3: Optical bench referencing. The CQS is mounted to translation stages on the optical bench, aligned to center ($\varepsilon_x = \varepsilon_y = 0$) using the micrometers. Micrometer positions, combined with the CMM-determined zero point, determine the absolute beam coordinates in the laboratory frame. For tilt, measurements are repeated at a second position along $L_z$.

4. Measurement Uncertainty, Noise, and Bandwidth

Empirical CQS performance is characterized as follows:

Metric	Value / Uncertainty	Conditions / Comments
Position readout standard uncertainty ($\sigma_{x,y}$)	±3.5 µm (1 σ)	Dominated by amplifier noise / mechanical play
Angle readout standard uncertainty ($\sigma_{\theta}$)	±12 µrad (1 σ)	Derived from $\sim$100 mm baseline differencing
Long-term drift	<5 µm (multi-day)	All axes, as measured in extended stability runs
Spectral density (position)	$\lesssim 0.11\,\mu\text{m}/\sqrt{\text{Hz}}$	White noise approximation at 1 kHz bandwidth
Spectral density (angle)	$\lesssim 0.38\,\mu\text{rad}/\sqrt{\text{Hz}}$	White noise approximation at 1 kHz bandwidth
Band of flat response	DC – 1 kHz	Quadrant preamplifier 3 dB corner, then roll-off

No increased $1/f$-like noise is observed above 1 mHz; mechanical drift contributions in the LISA band (0.1 mHz–1 Hz) are $<1\,\mu$m at lowest frequencies, corresponding to $<0.5\,\mu\text{m}/\sqrt{\text{Hz}}$ at 0.1 mHz. Two-point uncertainty was determined by repeated beam-centering over 100 s under stable, low-jitter ($\ll 1\,\mu$m RMS) conditions.

5. Implementation in Laboratory Systems

CQS units are attached to the glass-ceramic Clearceram optical bench with crossed flexure mounts integrating the micrometer drives. The alignment and calibration procedures are conducted under clean-room conditions with temperature stability to $<$0.1 K daily drift. Full system operation for ultimate noise performance occurs in vacuum (∼$10^{-5}$ mbar), reducing residual thermal coupling, with temperature noise $10^{-5}$ K/$\sqrt{\text{Hz}}$ at 1 mHz.

Readout electronics feature four low-noise transimpedance amplifiers (5 k$\Omega$ feedback, DC–100 kHz, $2\,\text{pA}/\sqrt{\text{Hz}}$ input-referred current noise), located external to the vacuum environment. Outputs are digitized (16-bit ADCs, up to 200 kS/s per channel), with all DPS normalization and calculation performed in FPGA hardware or post-processing software.

6. Role in Precision Interferometry and the LISA Three-Backlink Experiment

The CQS enabled the Three-Backlink Experiment’s core alignment, overlap, and stability tasks required for high-precision verification of candidate LISA backlink schemes (direct fiber, frequency-separated fiber, and free-beam link). Through direct referencing to the quasi-monolithic bench and micrometer-scale alignment, the system supports positional readout at the few-micrometer level and angular discrimination at $\sim 10\,\mu$rad, over the DC–100 kHz domain (Bischof et al., 16 Dec 2025).

The verified construction, as evidenced by achieved $\sim$15\,\text{pm}/\sqrt{\text{Hz}}$-equivalent testbed stability and absence of construction-limited noise, demonstrates the CQS’s utility in laboratory interferometer metrology for space-based gravitational wave detection and geodesy mission preparatory work.

7. Schematic Presentation and Instrument Visualization

Supporting figures in (Bischof et al., 16 Dec 2025) clarify the CQS design and metrological referencing:

• Photograph: Shows an assembled CQS, brass block, exposed quadrant wiring, and micrometer screws.
• CMM Calibration Schematic: Red datum planes define the block; a blue dot signifies the inferred photodiode center in the CMM frame.
• Beam-centering Sketch: Depicts the Gaussian beam illuminating the QPD, with coordinate referencing established by the visible outer block faces.

In summary, the Calibrated Quadrant Photodiode Singleton systematically combines a bare-die quadrant detector, CMM-calibrated mechanical referencing, and standard DPS electronics to deliver direct, accurate beam-vector measurements grounded in the optical bench metrology frame. It constitutes a critical infrastructure element for advanced interferometric alignment and stability at the micrometer and microradian level in optical metrology environments relevant to LISA and related research (Bischof et al., 16 Dec 2025).