Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

The effects of reduced bit depth on optical coherence tomography phase data

William A. Ling and Audrey K. Ellerbee

Open Access Open Access

Abstract

Past studies of the effects of bit depth on OCT magnitude data concluded that 8 bits of digitizer resolution provided nearly the same image quality as a 14-bit digitizer. However, such studies did not assess the effects of bit depth on the accuracy of phase data. In this work, we show that the effects of bit depth on phase data and magnitude data can differ significantly. This finding has an important impact on the design of phase-resolved OCT systems, such as those measuring motion and the birefringence of samples, particularly as one begins to consider the tradeoff between bit depth and digitizer speed.

© 2012 Optical Society of America

Full Article  |  PDF Article
More Like This
Performance comparison between 8- and 14-bit-depth imaging in polarization-sensitive swept-source optical coherence tomography

Zenghai Lu, Deepa K. Kasaragod, and Stephen J. Matcher
Biomed. Opt. Express 2(4) 794-804 (2011)

Performance of reduced bit-depth acquisition for optical frequency domain imaging

Brian D. Goldberg, Benjamin J. Vakoc, Wang-Yuhl Oh, Melissa J. Suter, Sergio Waxman, Mark I. Freilich, Brett E. Bouma, and Guillermo J. Tearney
Opt. Express 17(19) 16957-16968 (2009)

Spatially distributed successive approximation register (SDSAR) photonic ADCs based on phase-domain quantization

Moshe Nazarathy and Oded Shaham
Opt. Express 20(7) 7833-7869 (2012)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)
Fig. 1
Fig. 1 Vector plot of the measured OCT data (z-domain). I = signal vector, N = noise vector, and Y = the resultant. Components of the noise vector in quadrature with the signal vector lead to error δθ in the measured phase compared to the actual phase θ.

Download Full Size | PDF

Fig. 2
Fig. 2 Method to simulate reduced ADC resolution, including fractional bits. An unresampled interferogram iraw(k) is captured with a 12-bit ADC and modified in post-processing to produce an N + F-bit output, where 0 < F < 1. The NDFT (non-uniform DFT) combines resampling and Fourier transformation into a single operation.

Download Full Size | PDF

Fig. 3
Fig. 3 Behavior of a non-ideal (N + 1)-bit ADC. ne accounts for internal noise and thresholding errors of the ADC. Left: ideal (N + 1)-bit quantizer (i.e., a perfect rounding operation); the resulting ADC output has a resolution < N + 1 due to ADC imperfections described by ne. Right: the ideal quantizer can be replaced with an equivalent white-noise model in which QN is an uncorrelated additive noise.

Download Full Size | PDF

Fig. 4
Fig. 4 Demonstration of the two-step fractional requantizer from Fig. 2 to generate ENOBs of 3.2 (a and b) and 1.5 (c and d) bits from a 4-bit sinusoidal input sampled 32 times per period (gray). Simulated ADC signals appear in red. Step i (a and c): apply a pseudorandom noise sequence (blue) of the appropriate variance to the input to account for ADC non-idealities. Step ii (b and d): Quantize the resulting noisy sequence (red) to yield an output with the appropriate ENOB.

Download Full Size | PDF

Fig. 5
Fig. 5 Common-path OCT system used in this work. The sample comprised either a coverslip or a piezo-mounted mirror imaged from behind the coverslip. The reflectivity of the coverslip was changed by adding liquid droplets of varying refractive index.

Download Full Size | PDF

Fig. 6
Fig. 6 Displacement sensitivity vs ENOB for (a) glass-air, (b) glass-water, and (c) glass-gel interfaces. Error bars indicate one standard deviation of variation between trials. Theoretical curves are based on Eq. (7) and Eq. (9); the latter is clearly a better fit to the data. Experimental data and theoretical predictions converge with decreasing sample reflectivity or ENOB, as predicted. The arrows in (a)–(c) indicate the point at which the experimental sensitivity worsened by 3 dB. Note that plot axes differ to improve visibility of the data. The dotted black lines in (d) indicate the point at which SNR dropped by 1 dB relative to the SNR at 12 bits.

Download Full Size | PDF

Fig. 7
Fig. 7 1mm x 1mm views of the topography of a coverslip (CS) and neutral density filter (NDF) generated from phase using 12-bit, 8-bit, and 5-bit data. Due to the high reflectivity of the coverslip surface, quantization-induced phase noise is small, allowing accurate phase extraction even at very low bit-depths. Phase noise increases more rapidly with reduced ENOB when the reflectivity is lower, as for the NDF (the box shows an area of strong degradation with the arrow pointing to a ring that disappears in the 5-bit image). Note that scales are different in the top and bottom images.

Download Full Size | PDF

Fig. 8
Fig. 8 Displacement of a PZT driven at 100 Hz sinusoidal drive as calculated from 12-bit data. Fig. (b) shows the error in the displacement that would result if the waveform were instead generated using lower ENOBs (the waveform from 12-bit data is considered error-free and the waveforms from lower ENOBs are subtracted); the dashed horizontal lines show the RMS vibration noise (0.5 nm corresponds to 8% of the dynamic range). Except at very low bit depths, quantization noise is insignificant compared to vibration noise, since the sample reflectivity is large.

Download Full Size | PDF

Tables (1)

Tables Icon

Table 1 Accuracy of the fractional requantizer in generating desired ENOBs for unquantized (Case 1) and quantized (Case 2) sinusoidal inputs.

View Table

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

i ( k , t ) = A ( k ) R R R S cos ( 2 k n ( Δ z + δ z ( t ) ) ) ,
∠ I ( 2 n Δ z , t 2 ) − ∠ I ( 2 n Δ z , t 1 ) = 2 k 0 n ( δ z ( t 2 ) − δ z ( t 1 ) ) = 4 π n ( δ z ( t 2 ) − δ z ( t 1 ) ) λ 0 ,
σ n 2 = σ shot 2 + σ RIN 2 + σ dark 2 + σ amp 2 + σ DAQ 2 = σ det 2 + σ D A Q 2 .
σ q n 2 = Δ 2 12 = V F S 2 12 ( 2 2 B )
σ eff 2 = σ q n 2 + σ e 2 .
V F S 2 12 ( 2 2 E N O B ) = σ eff 2
σ D A Q 2 = σ eff 2
σ δ θ = 1 SNR ,
δ θ ≈ tan ( δ θ ) = N Q | I + N I | ≈ N Q | I |
σ δ θ = σ N 2 | I |
σ N + F 2 = V F S 2 12 ( 2 2 ( N + F ) ) , σ N + 1 2 = V F S 2 12 ( 2 2 ( N + 1 ) ) , σ e 2 = σ N + F 2 − σ N + 1 2               = V F S 2 12 ( 2 2 ( N + F ) ) − V F S 2 12 ( 2 2 ( N + 1 ) ) .
σ e , 12 2 = [ V F S 2 12 ( 2 2 ( N + F ) ) − V F S 2 12 ( 2 2 ( N + 1 ) ) ] − V F S 2 12 ( 2 2 ( 12 ) ) .
σ δ θ = P ( V F S 2 12 ( 2 2 E N O B ) + K 1 ( R S + R R ) + K 2 ( R S + R R ) 2 + σ dark 2 + σ amp 2 ) K 3 2 R S
σ p n 2 = σ a 2 + P σ q 2 2 | I | 2 + σ v 2 . σ q 2 = 2 | I | 2 ( σ p n 2 − σ v 2 ) − σ a 2 P .
ENOB = log ( V F S 2 12 σ q 2 ) / log ( 4 ) .
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use