Single-Shot Spectral Interferometry

• Single-shot spectral interferometry is a technique that captures full spectral amplitude and phase information from a single interferogram, eliminating the need for multi-shot scans.
• It employs diverse encoding strategies—such as spectral shearing, spatial encoding, and chirped probe methods—to enable measurements in applications from laser contrast metrology to ultrafast transient sensing.
• Advanced reconstruction algorithms, including Fourier and wavelet transforms, facilitate precise retrieval of temporal and spectral profiles with high dynamic range and low error.

Searching arXiv for recent and relevant papers on single-shot spectral interferometry. Single-shot spectral interferometry denotes a family of interferometric measurements in which a single recorded spectral interferogram, or a single camera frame containing spectrally encoded fringes, is used to recover spectral amplitude, spectral phase, temporal structure, contrast, or a related encoded observable. In the cited literature, this umbrella includes direct two-beam spectral interferometry, self-referenced spectral interferometry, spectral shearing interferometry in SPIDER-type geometries, supercontinuum spectral interferometry, and spatially encoded Michelson or common-path variants. Their common feature is the replacement of mechanical scanning or many-delay acquisition by spectral, spatial, or spatio-spectral encoding that is analyzable from one acquisition, which is especially important for low-repetition-rate, unstable, destructive, or non-reproducible sources (Palaniyappan et al., 2012, 0908.1245, Patel et al., 2019, Dulat et al., 2023).

1. Fundamental measurement principle

In direct spectral interferometry, an unknown field and a delayed reference field are superposed in the spectral domain. A representative form used for bright squeezed vacuum retrieval is

$$I(\omega) = |E_{BSV}(\omega) + E_{ref}(\omega)e^{-i\omega\tau}|^2,$$

where $E_{BSV}(\omega)$ is the unknown field, $E_{ref}(\omega)$ is the characterized reference, and $\tau$ is the delay (Kern et al., 22 Sep 2025). In self-referenced laser-contrast metrology, the same structure is written as

$$S(\omega) = |E(\omega) + E_{\text{ref}}(\omega)e^{i\omega\tau}|^2,$$

and inverse Fourier transformation of the measured interferogram produces a temporal-domain signal containing DC terms at zero delay and AC terms at $\pm\tau$, with the AC term encoding the cross-correlation between the test and reference pulses (Palaniyappan et al., 2012).

A second major branch is spectral shearing interferometry, in which the interferogram is formed not between two identical spectra separated only by delay, but between a spectrum and a spectrally shifted copy. For attosecond free-electron-laser pulse reconstruction, the interferogram is

$$S(\omega, \tau) = |E(\omega)|^2 + |E(\omega+\Omega)|^2 + 2 |E(\omega)| |E(\omega+\Omega)| \cos[\varphi(\omega) - \varphi(\omega+\Omega) + \omega\tau],$$

where $\Omega$ is the spectral shear and $\tau$ is the delay (Xiao et al., 2023). In SPIDER-type systems, the measured phase difference is then interpreted as a finite-difference approximation to the spectral phase derivative.

The essential operational idea is therefore not unique to a single apparatus. Single-shot behavior can arise from a large imposed delay that separates AC and DC terms in Fourier space, from a spatially varying shear that records many shears simultaneously, from a chirped probe whose instantaneous frequency maps time into wavelength, or from a fringe pattern whose transverse position becomes a proxy for wavelength (Palaniyappan et al., 2012, 0908.1245, Fordell, 2022, Lewis et al., 4 Dec 2025).

2. Experimental architectures and encoding strategies

A canonical linear implementation uses two beams: an unknown pulse and a fully characterized reference pulse. In the bright squeezed vacuum experiment, BSV and reference pulses were combined at a 20:80 beam recombiner, sent to a Si-based spectrometer with single-shot capability, and separated by a temporal delay of $\sim 3.05$ ps to generate well-resolved spectral fringes (Kern et al., 22 Sep 2025). This architecture is analytically simple because the reference amplitude and phase are known independently.

Self-referenced designs avoid an externally characterized reference. For high-dynamic-range laser contrast measurement, the test pulse is split into two arms, with one arm used to generate a reference pulse using low-gain optical parametric amplification; the reference and attenuated original pulse are recombined with a controlled delay and sent into an imaging spectrometer recorded on a high-dynamic-range, cooled CCD camera (Palaniyappan et al., 2012). For free-electron lasers, self-referencing is realized in a different way: the main amplifier generates the sample pulse, a chicane introduces the time delay, and an afterburner undulator with slightly detuned resonance generates the spectrally sheared reference pulse from the same electron bunch (Xiao et al., 2023).

SPIDER-derived single-shot systems encode many shears simultaneously. In SEA-CAR-SPIDER, two ancilla beams generated from the test pulse are spatially chirped, one ancilla is spatially inverted about $E_{BSV}(\omega)$0, both are overlapped with the test pulse in a nonlinear crystal, and the resulting two-dimensional interferogram contains multiple shears, the spectral amplitude of the test pulse, and the reference phase in one shot (0908.1245). The key relation is that the shear varies continuously with transverse position, $E_{BSV}(\omega)$1, so each detector row corresponds to a different shear.

Supercontinuum spectral interferometry employs a chirped probe and reference. In SSSI, the pump-induced phase modulation is encoded into the interferometric phase difference between perturbed and unperturbed supercontinuum pulses, and the standard apparatus can be used without hardware modification when chirp retrieval is transferred to data analysis (Vu et al., 2018, Patel et al., 2019). A related but distinct use of a chirped supercontinuum appears in all-optical time interpolation, where the arrival time of a timing pulse is encoded into a localized spectral feature produced by cross-phase modulation on the time-stretched supercontinuum (Fordell, 2022).

Single-shot spectral encoding can also be realized in a Michelson interferometer without scanning mirrors. In an adaptive optics-enhanced Michelson interferometer, a reflective spatial light modulator replaces one mirror. Even when a constant phase profile is applied to the SLM, the fringes across the interferometer output beam are shifted in wavelength across the transverse axis, so a single CCD image can encode the spectrum of a narrow-band source after calibration (Lewis et al., 4 Dec 2025).

3. Reconstruction algorithms, calibration, and inverse problems

The most common reconstruction route is Fourier separation of interference terms. In the Takeda-style processing used for BSV pulse retrieval, each single-shot interferogram is Fourier transformed from the frequency domain into the delay domain, the AC term at $E_{BSV}(\omega)$2 is isolated by windowing, and an inverse transform returns a complex spectral product proportional to $E_{BSV}(\omega)$3. Because the reference is fully known, the spectral phase of the unknown field is obtained directly, and inverse Fourier transformation then yields the temporal electric field profile and intensity profile (Kern et al., 22 Sep 2025). The same DC/AC separation underlies self-referenced laser contrast retrieval, where the AC term directly provides the cross-correlation of the laser pulse with the reference pulse provided there is enough time-delay imposed between them (Palaniyappan et al., 2012).

SPIDER-type retrieval uses phase-difference concatenation rather than direct temporal cross-correlation. In SEA-CAR-SPIDER, 2D Fourier filtering isolates the interferometric sideband, the calibration phase $E_{BSV}(\omega)$4 is recovered either from the $E_{BSV}(\omega)$5 row or by symmetry-based averaging, and the standard SPIDER concatenation retrieval algorithm is then applied for each shear (0908.1245). Because the ancilla-only trace contains the shear slope, upconversion frequency, and reference phase position, all calibration parameters are obtained from a single calibration trace.

For chirped supercontinuum spectral interferometry, the main inverse problem is often the unknown probe spectral phase. One formulation writes

$E_{BSV}(\omega)$6

with $E_{BSV}(\omega)$7 expanded in dispersion coefficients such as $E_{BSV}(\omega)$8 and $E_{BSV}(\omega)$9. The proposed criterion is that, for the correct chirp parameters, the retrieved temporal modulations from different pump-probe delays overlap after time shifting; the misalignment metric

$E_{ref}(\omega)$0

is then minimized, including by genetic algorithm implementations (Vu et al., 2018, Patel et al., 2019).

FEL self-referenced SSI introduces a different retrieval strategy because structured spectra can make Fourier-only extraction noise-sensitive. The cited method uses a Wavelet Transform to generate time-frequency magnitude and phase topographies, identifies the ridge in the magnitude map, extracts the phase difference $E_{ref}(\omega)$1, subtracts the known delay term, and numerically inverts to recover the original spectral phase (Xiao et al., 2023).

The Michelson-SLM spectroscopy variant depends more explicitly on empirical calibration. A known narrow-band source is measured at multiple spatial points across a fringe using a fiber optic spectrometer while the fringe is imaged on a CCD; the correlation between fringe maxima positions and measured spectral peaks establishes a position-wavelength calibration curve, after which spectra within the calibration range can be inferred from CCD images alone (Lewis et al., 4 Dec 2025). This indicates that single-shot operation and calibration-free operation are not synonymous.

4. Principal measurement modalities

One major use of single-shot spectral interferometry is temporal contrast metrology. In self-referencing spectral interferometry, inverse Fourier transformation of the spectral interferogram directly provides the cross-correlation of the laser pulse with the reference pulse, enabling single-shot 60 dB dynamic range laser contrast measurement; for full-system, high-energy shots, the reported dynamic range was $E_{ref}(\omega)$2 dB, and the method was cross-calibrated against scanning third-order autocorrelator measurements (Palaniyappan et al., 2012). A related high-power-laser application is self-referenced spectral interferometry with extended time excursion, used after a plasma mirror to resolve the pulse rising edge and the plasma mirror trigger point. In that implementation, the temporal resolution was $E_{ref}(\omega)$3 fs, the time window extended from a few tens of fs to $E_{ref}(\omega)$4 picoseconds, and the dynamic range reached $E_{ref}(\omega)$5 (Obst et al., 2019).

A second major modality is full pulse-field retrieval. The BSV experiment demonstrated full single-shot retrieval of both spectral intensity and phase for femtosecond bright squeezed vacuum pulses using a fully characterized coherent-state reference pulse. Across 1009 analyzed single-peak BSV shots, the group delay was consistent near the central frequency, the average pulse duration was $E_{ref}(\omega)$6 fs, and the shot-to-shot standard deviation was $E_{ref}(\omega)$7 fs. The interferograms also exhibited a characteristic nodal structure associated with a random phase ambiguity of $E_{ref}(\omega)$8 rad (Kern et al., 22 Sep 2025). In the FEL case, the method reconstructed temporal profile and phase of attosecond x-ray FEL pulses with an error of only a few-percent-level; in simulations of soft x-ray attosecond pulses, the pulse-duration reconstruction error was $E_{ref}(\omega)$9 rms over 60 shots (Xiao et al., 2023).

A third modality is ultrafast transient sensing. Single-shot supercontinuum spectral interferometry measures ultrafast transients in the complex index of refraction using chirped probe and reference pulses (Vu et al., 2018). The simplified variants show that, with as few as two time-delayed pump-probe shots, the probe chirp up to third-order dispersion and the pump-induced modulation can be retrieved without pre-characterization, and a practical single-pump-probe-shot method is possible when probe and reference pulses are identical, temporally overlap, and both are modulated within the overlap region (Patel et al., 2019).

Single-shot spectral interferometry is also used for spectroscopy in the narrow-band regime. In the adaptive optics-enhanced Michelson interferometer, the transverse position of a fringe maximum becomes a proxy for wavelength because the fringes are inherently shifted in wavelength across the output beam. A single CCD image then provides rapid single-snapshot spectroscopy, while a time-varied SLM phase profile enables multi-step spectroscopy with lower noise, higher resolution, and better contrast. The cited limitation is that the source bandwidth should not be so broad that a single point on the fringe corresponds to multiple spectral peaks; the method is described as ideal for sources with $\tau$0 nm bandwidth (Lewis et al., 4 Dec 2025).

5. Multidimensional and spatially encoded extensions

Single-shot spectral interferometry has been generalized from one-dimensional pulse retrieval to spatio-temporal metrology. TG-SSSI, or transient-grating single-shot supercontinuum spectral interferometry, measures the space- and time-resolved spatiotemporal amplitude and phase of an ultrashort laser pulse from a single-shot 2D interferogram with spatial and wavelength axes. A structured pulse and an interferometric reference generate a transient nonlinear index grating in a fused silica witness plate; a synchronized supercontinuum probe traverses the grating, and the phase-shifted probe is interfered with a delayed supercontinuum reference in an imaging spectrometer. Fourier analysis, low-pass filtering, and high-pass demodulation yield both the intensity envelope $\tau$1 and the phase $\tau$2, and the method was demonstrated on short pulses carrying spatiotemporal optical vortices (Hancock et al., 2020).

A further extension performs single-shot three-dimensional spatio-temporal and spatio-spectral measurements by spatial multiplexing. In relativistic plasma optics metrology, the reference and probe beams are sampled by a lenslet array, different spatial portions are routed through a fiber array to dedicated spectrometers, and the spectral interference in each channel is recorded simultaneously. Combining all channels yields $\tau$3, and Fourier transforming the spectral data yields $\tau$4, enabling reconstruction of pulse-front structure and plasma-induced modulations over the full field in one shot (Dulat et al., 2023).

Spatial encoding can also replace spectral dispersion in more specialized settings. The Michelson-SLM system exploits the fact that the spectral peak measured at different fringe locations traces a “teardrop” shape whose width depends on the spectral bandwidth of the source, the relative tilt and path difference between the interferometer arms, and the divergence of the beam. This spatial-spectral trace is then used for fast single-snapshot spectroscopy and suggests an interferometric route toward hyperspectral imaging (Lewis et al., 4 Dec 2025).

AI-enhanced common-path interferometry extends the same single-shot logic to broadband phase sensing and hyperspectral imaging. In general polarization common-path interferometry, orthogonally polarized reference and sensing beams are generated before the sample, recombined by a polarizer at $\tau$5, and processed by Fourier extraction of the sideband phase. Deep neural autoencoders operating on second-order derivative maps of the phase profile are used to detect anomalies, while a ConvNeXt V2 model is used for single-shot and real-time tracking of phase variation with minimized noise. The reported outcome is an order of magnitude improvement in phase stability compared to state-of-the-art interferometry techniques, alongside hyperspectral single-cell dispersion imaging (Behrouzi et al., 2 Jan 2026). This suggests that single-shot spectral interferometry is increasingly coupled to computational post-processing rather than being defined solely by the optical front end.

6. Performance envelope, constraints, and recurring methodological issues

The principal advantage across the literature is the removal or reduction of scanning. In the Michelson-SLM implementation, adaptive optics enables interferometer-based spectroscopy without the moving parts necessary for scanning the interferometer arms (Lewis et al., 4 Dec 2025). In SEA-CAR-SPIDER, all shears and calibration parameters are acquired in one shot, eliminating moving parts and frequent recalibration (0908.1245). In laser-contrast and plasma-optics experiments, single-shot capability is critical because the relevant systems are low-repetition-rate or strongly fluctuating, so multi-shot averaging can obscure the event of interest (Palaniyappan et al., 2012, Dulat et al., 2023).

The performance envelope is highly application-specific. Contrast metrology emphasizes dynamic range and temporal separation of AC and DC terms; spectroscopy emphasizes bandwidth limits, contrast, and calibration validity; pulse retrieval emphasizes reference quality or self-reference accuracy; spatio-temporal extensions emphasize spatial multiplexing density and probe bandwidth. The cited studies therefore report very different headline figures: 60 dB single-shot dynamic range for pulse contrast (Palaniyappan et al., 2012), $\tau$6 dynamic range with $\tau$7 fs temporal resolution for SRSI-ETE (Obst et al., 2019), few-percent-level reconstruction error for FEL pulses (Xiao et al., 2023), and 4–5 fs short-term jitter, approaching the 1 fs level with stabilization, for time interpolation using a chirped supercontinuum (Fordell, 2022).

Several recurrent constraints are explicit. Adequate delay is required so that the AC term is sufficiently isolated from the DC term in Fourier space (Palaniyappan et al., 2012). In FEL self-referenced SSI, spectral shear and time delay improve phase retrieval but are limited by chicane-induced bunching degradation (Xiao et al., 2023). In the Michelson-SLM spectroscopy method, the one-to-one position-wavelength mapping is lost if the bandwidth is too broad, and the method is stated to be ideal for sources with $\tau$8 nm bandwidth (Lewis et al., 4 Dec 2025). In the single-shot SSSI variant without probe pre-characterization, probe and reference must be identical and temporally overlapped, and the pump-induced phase shift must lie within the overlap region (Patel et al., 2019). For spatially multiplexed plasma metrology, spatial resolution is limited by the number of spectrometers, fibers, and the lenslet-array pitch (Dulat et al., 2023).

A recurring methodological issue is the relation between “single-shot” and “single-interferogram.” The literature contains true one-frame reconstructions, reduced-shot protocols requiring two delayed snapshots, and single-shot variants that become valid only under additional overlap or calibration conditions (Vu et al., 2018, Patel et al., 2019). This suggests that, in current usage, single-shot spectral interferometry is best understood as a measurement class that compresses information acquisition into one event of the physical system under study, even when auxiliary calibration traces, pre-characterized references, or computational correction stages remain necessary.

Across these variants, single-shot spectral interferometry functions less as a single instrument than as a general metrological strategy: encode spectral or temporal information into an interferogram that is separable by delay, shear, spatial coordinate, polarization, or multiplexed channels; reconstruct the encoded phase or amplitude with Fourier, wavelet, concatenation, optimization, or calibration-based inversion; and thereby obtain shot-resolved information that would otherwise require scanning, repetitive measurements, or nonlinear diagnostics (0908.1245, Xiao et al., 2023, Lewis et al., 4 Dec 2025).