Spectrum-Guided Depth Division Multiplexing

• Spectrum-Guided Depth Division Multiplexing (SGDDM) is a method that employs spectral-domain modulation to encode and separate overlapping depth channels in applications like computer-generated holography and spectral-domain OCT.
• In full-color CGH, SGDDM uses learnable circular masks to shape the angular spectrum, enabling simultaneous RGB reconstruction at distinct axial depths without sacrificing frame rate.
• In SD-OCT, SGDDM applies deterministic phase ramp tagging to multiplex signals from multiple anatomical depths onto a single detector, achieving high SNR and precise depth separation.

Spectrum-Guided Depth Division Multiplexing (SGDDM) denotes a class of depth-multiplexing strategies in which spectral-domain control is used to separate channels that would otherwise overlap axially. In the cited arXiv literature, the term is used for a frequency-domain modulation strategy in high-speed full-color video computer-generated holography (CGH), where learnable masks jointly optimize hologram phase and angular spectrum for simultaneous RGB reconstruction at distinct depths (Zhang et al., 27 Aug 2025), and for a single-modulator depth-multiplexing strategy in spectral-domain optical coherence tomography (SD-OCT), where deterministic phase ramps act as spectral tags for multiple reference-arm delays and enable computational demixing on a single detector (Meng et al., 2023). In both settings, SGDDM is introduced to avoid the penalties of naive multiplexing: color crosstalk and depth overlap in CGH, and hardware complexity or range limitations in SD-OCT.

1. Conceptual scope and shared principle

Both uses of SGDDM are organized around the same operational idea: depth channels are not treated as independent acquisitions, but are encoded so that a single measurement can later be separated by spectral or frequency-domain structure. The encoded channels differ by application. In CGH, the channels are the three color components $r$, $g$, and $b$, each assigned to a different reconstruction plane $z_r$, $z_g$, and $z_b$. In SD-OCT, the channels are three anatomical depth regions—retina, pupil/lens, and cornea—mapped to different reference-arm delays.

Domain	Multiplexed channels	Spectral guidance mechanism
Full-color CGH	$R$, $G$, $B$ at distinct axial depths	Learnable circular masks $M_c(f_x,f_y)$ shaping the hologram spectrum
SD-OCT	Retina, pupil/lens, cornea	Distinct line-to-line phase ramps $g$0 imposed by a single reference galvanometer

The shared objective is simultaneous acquisition or display without the dominant penalty of conventional alternatives. In CGH, time multiplexing (TM) eliminates inter-channel overlap because each wavelength is displayed in a separate time slot, but incurs a $g$1 frame-rate reduction. Depth-division multiplexing (DDM) avoids that temporal penalty but becomes susceptible to crosstalk when the depth of field (DOF) is large. In SD-OCT, existing depth-multiplexing methods typically require multiple light modulation units or detectors for simultaneous imaging across depths, increasing complexity and cost. SGDDM is introduced in each case as a way to preserve simultaneity while restoring separability (Zhang et al., 27 Aug 2025, Meng et al., 2023).

2. SGDDM in full-color computer-generated holography

In the holographic setting, SGDDM is defined as a frequency-domain modulation strategy that jointly optimizes the hologram phase and its angular spectrum so that three color channels can be multiplexed into a single phase-only hologram and reconstructed at distinct axial depths with minimal color crosstalk—without sacrificing the spatial light modulator’s native frame rate (Zhang et al., 27 Aug 2025).

The motivation arises from a specific failure mode of learning-based CGH. Deep networks trained with intensity-only losses tend to produce smooth phase patterns, especially from uniform or low-frequency initializations. By Parseval’s theorem, smooth spatial phase implies energy concentrated at low spatial frequencies. Low-frequency spectra diffract at small angles, given by $g$2, yielding a small numerical aperture (NA) and large DOF. In DDM, each color channel is assigned to a different focal depth $g$3 and reconstructed simultaneously from a single hologram. If the phase has a large DOF, the reconstruction for one color remains in focus across neighboring depths, and other wavelengths may form in-focus replicas at unintended planes. The result is axial overlap and therefore color crosstalk.

The forward model uses the angular spectrum method (ASM). With a phase-only SLM field

$g$4

the propagated field for channel $g$5 at target depth $g$6 is

$g$7

with transfer function

$g$8

The reconstruction intensity is

$g$9

The key SGDDM intervention is the color-wise mask $b$0. Operationally, the hologram phase is Fourier-transformed and the resulting spectrum is multiplied by a color-specific mask. The mask shifts and/or expands spectral support, effectively applying an off-axis linear phase ramp and increasing phase-gradient energy. Larger diffractive angles imply larger NA, and larger NA reduces DOF. The intended consequence is sharper depth selectivity, so RGB reconstructions do not overlap axially.

This mechanism distinguishes SGDDM from conventional DDM, which simply superposes RGB constraints at different depths, and from prior band-limiting or shift-multiplexing approaches that sacrifice resolution or require external optics. In the reported formulation, SGDDM is a learnable, in-silico spectral guidance method that does not add optical components.

3. Optimization, mask parameterization, and holographic operating regime

SGDDM in CGH is integrated with a learning-based phase generator, HoloMamba, described as a lightweight asymmetric Mamba-Unet architecture that explicitly models spatial-temporal correlations across video sequences. The generator produces one phase-only hologram $b$1 per frame, and SGDDM applies spectral guidance during training and forward propagation (Zhang et al., 27 Aug 2025).

For each frame, the single phase $b$2 must satisfy three simultaneous constraints:

$b$3

where $b$4 denotes the target intensity for channel $b$5.

The paper’s implementation uses two fidelity terms. The reconstruction loss is

$b$6

and the focal frequency loss is

$b$7

with dynamic weight

$b$8

The total loss used in the paper is

$b$9

The data also describes compatible extensions, including a crosstalk penalty $z_r$0, a spectral shaping regularizer $z_r$1, and temporal consistency term $z_r$2, but explicitly notes that the paper’s implementation trains with $z_r$3.

Each $z_r$4 is parameterized as a learnable circular mask centered at $z_r$5 with radius $z_r$6. Applying $z_r$7 in the Fourier domain is equivalent to adding a linear phase ramp in the spatial domain:

$z_r$8

so that

$z_r$9

During training, the binary mask is replaced with a soft surrogate

$z_g$0

with $z_g$1 annealed from $z_g$2 up to $z_g$3.

Depth separation is governed by the approximate relation

$z_g$4

and the reported suppression criterion

$z_g$5

SGDDM learns $z_g$6 to increase $z_g$7, thereby easing this constraint.

At the system level, one phase-only hologram $z_g$8 is displayed per frame at the SLM’s native refresh rate, and with simultaneous RGB illumination the three wavelengths reconstruct at $z_g$9, $z_b$0, and $z_b$1 in a single shot. Inference is training-free: given incoming frames, HoloMamba produces $z_b$2, which is sent directly to the SLM. The reported operating point is FHD $z_b$3 full-color holographic video at over $z_b$4 FPS; more specifically, HoloMamba reaches PSNR $z_b$5 dB and SSIM $z_b$6 while running at $z_b$7 FPS on FHD, more than $z_b$8 faster than Divide-Conquer-and-Merge Strategy. The reported SGDDM effect is restoration of accurate colors in simultaneous full-color reconstructions, including numeric and optical demonstrations and a single-shot AR demonstration combining real objects and holograms.

4. SGDDM in depth-multiplexing spectral-domain OCT

In the SD-OCT setting, SGDDM is realized in a single interferometer with one sample arm and a reference-arm set, using a single modulation unit for depth encoding (Meng et al., 2023). The line-scan camera records the interferometric spectrum $z_b$9 at each lateral position. A galvanometer scanner placed in the reference-arm set imposes distinct deterministic phase ramps across the transverse dimension of the B-scan for multiple reference arms. These ramps serve as spectral tags for different depth channels, and the multiplexed spectrum is then computationally demixed.

The optical configuration reported in the paper includes an SLD at $R$0 nm with $R$1 nm, a spectrometer with holographic grating Wasatch Photonics HD 1800 and spectral resolution $R$2 nm, and a Teledyne DALSA Spyder3 1k line-scan camera operating at $R$3 exposure for a $R$4 kHz A-scan rate. The reference arm is split into three arms using two cube beam splitters, with adjustable optical path lengths targeting the retina, pupil/lens region, and cornea. A single Thorlabs GVS011 galvanometer acts as the modulation unit. A $R$5 beam reducer and a lenslet array with $R$6 mm $R$7 $R$8 mm pitch route the delayed reference beams onto correct paths.

The reported reference-arm depths in reconstructed $R$9-space are $G$0, $G$1, and $G$2. By multiplexing several reference-arm delays, the system covers the full axial length of the eye, with optical path length $G$3 mm, corresponding to $G$4 mm geometrical length, compared with a single-arm imaging range of only $G$5 mm within $G$6 dB roll-off.

The SD-OCT interferogram is modeled as

$G$7

Depth-specific tagging is created by off-center beam incidence on the reference scanner. The modulated reference-arm path change is

$G$8

and near $G$9,

$B$0

The line-to-line phase slope is therefore

$B$1

For $B$2 channels, the prescribed phase shifts are

$B$3

with required off-center distances

$B$4

For $B$5, the system uses $B$6 mm, $B$7 mm, and $B$8 mm. With $B$9 nm and scanner step size $M_c(f_x,f_y)$0 per line, the measured slopes are $M_c(f_x,f_y)$1 rad/line, $M_c(f_x,f_y)$2 rad/line, and $M_c(f_x,f_y)$3 rad/line, placing the spectra centers at approximately $M_c(f_x,f_y)$4, $M_c(f_x,f_y)$5, and $M_c(f_x,f_y)$6 in the lateral Fourier domain.

5. Computational demixing, reconstruction, and reported measurements

The multiplexed SD-OCT measurement across lateral lines is written as

$M_c(f_x,f_y)$7

where $M_c(f_x,f_y)$8 is the lateral line index and the tags $M_c(f_x,f_y)$9 are separable by Fourier analysis along $g$00 (Meng et al., 2023).

The demixing procedure first applies standard SD-OCT preprocessing such as dark subtraction, spectral flattening, resampling to uniform $g$01, and optional dispersion compensation. A lateral Fourier transform is then computed:

$g$02

Because each channel occupies a distinct lateral frequency, windowing of the lateral spectrum isolates the depth channels:

$g$03

For three channels, the paper uses equal partitions of the $g$04–$g$05 phase quadrant: $g$06–$g$07, $g$08–$g$09, and $g$10–$g$11.

Because galvanometer vibration introduces imperfect isolation, the paper adds a heuristic decorrelation step. After initial demixing, define

$g$12

For each pixel, let $g$13; then assign

$g$14

optionally masked by a binary $g$15 indicating correlations exceeding a threshold $g$16. The reported effect is substantial reduction of cross-talk.

The quantitative operating point is explicit. Three channels are acquired concurrently on a single line-scan camera. The measured axial resolution is $g$17. Peak SNR exceeds $g$18 dB at all three depths at $g$19 exposure. The system measures axial length as an optical path length of $g$20 mm, converted to a geometrical axial length of $g$21 mm following Olsen’s conversion; the benchmark Zeiss IOL Master 700 measures $g$22 mm, a difference of approximately $g$23 mm. The paper also reports CCT, AQD, and ACD as in agreement with IOL Master 700, though without numeric breakdown in the text.

The CGH paper reports an analogous computational and system-level outcome for holographic display: SGDDM broadens and shifts spectral distributions to mitigate crosstalk compared with unguided DDM, while HoloMamba supplies the phase generator that sustains FHD generation at over $g$24 FPS and preserves the single-shot nature of simultaneous RGB display (Zhang et al., 27 Aug 2025).

6. Trade-offs, limitations, and interpretive significance

In both domains, SGDDM introduces an explicit trade-off between separability and resource efficiency. In holography, stronger spectral expansion improves color separation by increasing NA and reducing DOF, but can increase speckle and lower diffraction efficiency because energy outside the mask is discarded. Smaller radii can reduce speckle and improve efficiency, but enlarge DOF and increase crosstalk. Hard-edged masks can cause ringing, so the soft sigmoid boundary and gradual $g$25 annealing are used to mitigate ringing and Gibbs artifacts. Residual limitations remain for highly textured content, very large depth separations, extreme chromatic differences, and scenes with tight depth spacing. The reported assumptions include coherent multi-wavelength illumination, a phase-only SLM with adequate refresh rate, and accurate propagation-model calibration (Zhang et al., 27 Aug 2025).

In SD-OCT, the principal drawbacks are reduced spectrometer dynamic range when multiple arms are captured simultaneously, cross-talk from mechanical vibration and imperfect lateral-frequency isolation, and the alignment burden of a free-space reference-arm prototype. Scaling beyond three channels is described as possible by refining the partition of the $g$26–$g$27 phase quadrant, but practical limits arise from channel separation in lateral frequency, SNR per channel, dynamic range, and sensitivity to mechanical jitter. Future directions noted in the paper include more robust tagging, improved calibration of $g$28 and $g$29, compressed sensing or adaptive demixing, and learned demixing (Meng et al., 2023).

A recurrent misunderstanding is to treat SGDDM as a single standardized method. The cited literature instead uses the name for two domain-specific implementations with different measurement physics: angular-spectrum shaping of a phase-only hologram in CGH, and line-to-line phase-ramp tagging of reference-arm interferometric channels in SD-OCT. What unifies them is not a shared optical layout or optimizer, but a shared principle: spectral guidance is used as a control variable for depth selectivity. This suggests that SGDDM is best understood as a multiplexing framework in which spectral structure is deliberately engineered so that simultaneous channels can be separated without resorting to serial acquisition, multiple modulators, or multiple detectors.