Lock-In Subtraction: The Math That Subtracts 1000 W/m² of Sunshine

Daylight EL (the core capability of SC-DEL-Portable / SC-DEL-Drone) seems magical — imaging a signal one millionth as bright as sunshine, under 1000 W/m² of direct sun. It isn't magic; it's math. This article walks engineers through the lock-in subtraction algorithm and MVCreate's engineering implementation.

1. Problem statement: SNR of -60 dB

Let's quantify the problem:

• Solar irradiance (direct): 1000 W/m²; ~5 W/m² near 1100 nm;
• EL irradiance: ~50 μW/m² at the camera plane (full operating current);
• SNR: 50 μW / 5 W = 10⁻⁵, i.e. -50 dB.

A narrow bandpass filter (1100 ± 15 nm) suppresses solar by 95% to 0.25 W/m², leaving SNR ≈ 50 μW / 0.25 W = 2 × 10⁻⁴ ≈ -37 dB.

At -37 dB, the signal is fully buried in noise — a CMOS or InGaAs camera sees nothing of EL. The algorithm must lift SNR above ~+10 dB to image. That's lock-in subtraction.

2. The physics of lock-in detection

Lock-in detection (developed in the 1940s) is a weak-signal technique whose core idea is use frequency to separate signal from noise.

Sunlight is almost DC — intensity varies slowly (clouds move on a seconds-to-tens-of-seconds scale). If we modulate EL onto a specific high frequency (say 5 Hz), in the frequency domain EL becomes a sharp peak at 5 Hz while sunlight is broadband DC – 0.1 Hz.

At 5 Hz only EL exists — as long as the camera can sense 5 Hz variations, it can "see" EL.

3. MVCreate's engineering implementation

In theory it's simple — pulse current, sync camera, subtract. In engineering there are four key decisions:

3.1 Modulation frequency

Too low (<1 Hz): solar low-frequency wobble (clouds, wind) leaks into the signal band;
Too high (>50 Hz): camera frame rate can't follow, and the cell's thermal response lags.

We picked 1–10 Hz adaptive:

• Stable clear day: 1–3 Hz (sufficient to dodge solar low-freq);
• Cloudy day: 5–10 Hz (dodges cloud flicker).

3.2 Sync precision

Current pulses must align with camera exposure to sub-millisecond precision — otherwise subtraction errors creep in. We use FPGA hardware triggers (~100 ns precision) — sync error is negligible.

3.3 Phase-sensitive detection vs simple subtraction

Naïve subtraction ("on frame – off frame") only uses the fundamental — it's not "real" lock-in.

We use sinusoidal in-phase/quadrature phase-sensitive detection:

1. Apply quasi-sinusoidal current (not a square pulse);
2. Capture multiple frames per cycle (8–16);
3. Compute inner products with sin/cos references at the modulation frequency;
4. Extract amplitude + phase.

The phase information additionally rejects incoherent noise.

3.4 Multi-cycle accumulation

A single cycle still isn't enough; accumulate many cycles:

• Accumulating N cycles: signal grows N× (coherent);
• Noise grows √N (incoherent);
• SNR improves by √N.

Accumulating 100 cycles (10 s of data at 10 Hz) gives +20 dB.

4. Final SNR uplift

Stacking everything:

Final SNR: +13 dB — sufficient for sharp imaging. The number looks simple; behind it are five layers of optimization.

5. Versus competitor algorithms

Industry daylight EL algorithms split into three camps:

Camp 1: filter-only (no lock-in)

Only bandpass + strong EL current; no phase. SNR ~ -20 dB, image quality poor, fine defects invisible.

Camp 2: simple subtraction

"On frame – off frame" — equivalent to fundamental-only square-pulse lock-in. SNR ~ +5 dB — major defects visible, fine microcracks and broken-finger details still missed.

Camp 3: PSD (MVCreate)

Sinusoidal modulation + PSD + multi-cycle accumulation. SNR +13 dB — close to 60–70% of nighttime EL.

The gap is most visible on small-scale defects: 50 μm microcracks invisible to camps 1 & 2 are reliably detected by PSD.

6. Future directions: adaptive modulation + deep denoising

Lock-in isn't the end. Two ongoing directions:

6.1 Adaptive modulation frequency

Real-time tuning based on irradiance, wind speed, cloud dynamics — dodge instantaneous solar noise peaks. E.g., if a cloud-induced 0.5 Hz oscillation appears, jump to 8 Hz modulation.

6.2 Deep-learning-assisted denoising

The lock-in output still has residual noise with a specific statistical signature (Gaussian + Poisson mix). Train a U-Net denoiser on lock-in outputs as a post-process; add another +5–8 dB.

Targeted for SC-DEL series firmware in H2 2026.

7. Practical reminders for customers

Knowing the principle, here are field tips for daylight EL:

1. Avoid windy days — rack vibration introduces noise near the modulation frequency; SNR drops;
2. Avoid solar noon — vertical-incidence sun is the harshest; morning/evening (oblique sun) helps;
3. Cloudy isn't always worse — stable overcast can outperform direct sun, but drifting clouds add flicker — worse;
4. Don't fiddle with parameters — modulation frequency and accumulation count are auto-optimized by the algorithm; manual override hurts.

For algorithm demos or a side-by-side, contact MVCreate at +86 159-5048-9233.

Originally published by Vision Potential (Nanjing MVCreate Intelligent Technology Co., Ltd.). Reproductions must credit the source.