How sensor bit depth and modulation frequencies affect depth measurement precision for a single pixel
Depth Precision vs Distance
Y:
Sensor Parameters
ADC Bit Depth
Modulation Frequencies
Modulation Contrast at 1 m
0.50
Fraction of ADC full-scale occupied by the AC modulation amplitude at 1 m reference distance.
Signal amplitude falls off as 1/d² (inverse-square law).
Background DC Offset (LSB)
0.0
Shift of DC level from ADC mid-scale, in LSB units. Models ambient light variation,
dark current drift, etc. At 0, Ibg sits exactly at mid-scale (half-integer).
Non-zero values break the quantization symmetry.
Read Noise (LSB)
0.0
Gaussian read noise in ADC levels, added to each raw sample before quantization.
At 0, precision is purely quantization-limited.
Display Range
Max depth (m)
10
Y min (mm)
Y max (mm)
Analytical Reference
These formulas show the linearized analytical model (continuous atan2 approximation).
The plotted curves use Monte Carlo simulation of the actual quantized pipeline,
which captures clipping, discrete atan2, and noise dithering that these formulas miss.
1. Emitted illumination
2. Four-tap correlation samples
3. Phase & depth recovery
4a. Unambiguous range (single freq.)
4b. Multi-frequency unambiguous range
5. Amplitude at distance d (ADC levels)
6. Per-sample noise (ADC levels)
7. Phase precision (error propagation through atan2)
8. Depth precision (single freq.)
9. Multi-frequency MLE combination
Monte Carlo simulation: Curves are computed by running
the actual measurement pipeline — continuous samples are
quantized to B-bit integers, sensor noise is added before
quantization, and integer differences are fed into atan2.
This captures effects that analytical error propagation misses:
discrete atan2 output from integer I/Q inputs,
ADC clipping at close range, and
noise dithering of quantization bins (a small amount of
noise can actually improve precision by breaking the
discrete grid).
Multi-frequency combination uses inverse-variance weighting
of per-frequency MC precisions. Phase unwrapping reliability
(interaction between GCD and noise) is not yet modeled.