Transient Phase Microscopy

• Transient phase microscopy is a time-resolved imaging method that quantifies rapid optical phase shifts induced by variations in refractive index and sample geometry.
• It employs advanced interferometric and holographic techniques, such as pump-probe setups and synthetic holography, to capture ultrafast phenomena including photoexcitation, thermal diffusion, and mechanical vibrations.
• The technique offers practical insights for materials science, biological imaging, and chemical analysis by providing nanometric spatial resolution and femtosecond to microsecond temporal resolution.

Transient phase microscopy is a class of time-resolved imaging modalities that resolve fast, often picosecond- to millisecond-scale, changes in optical phase induced by transient physical, chemical, or mechanical processes in a specimen. These transient phase shifts reflect changes in the local refractive index, sample geometry, or both, typically caused by ultrafast processes such as photoexcitation, mechanical vibration, thermal diffusion, or phase segregation of materials. Quantitative access to these phase changes at high temporal and spatial resolution enables the direct interrogation of ultrafast molecular dynamics, nanomechanical motion, bond-selective photophysics, and structure–function relationships in both materials and biological systems.

1. Theoretical Foundations of Transient Phase Imaging

Transient phase microscopy leverages the relationship between the measured optical phase and temporally evolving sample properties. For a probe pulse of wavelength $\lambda$ traversing or reflecting from a region with a space– and time–dependent refractive index $n(x, y, z, t)$ and geometric thickness $L(x, y, t)$, the induced phase shift is

$$\Delta\phi(x, y, t) = \frac{2\pi}{\lambda}\int_0^{L(x,y,t)} \big[n(x, y, z, t) - n_0\big]\,dz + \frac{2\pi}{\lambda}n_0\,\Delta L(x,y,t)$$

Two main mechanisms typically underlie pump/probe–induced phase transients:

• Thermo-optic effect (TOE): local absorption (e.g., by resonant mid-IR) raises the temperature $\Delta T$, shifting the refractive index by $dn/dT \cdot \Delta T$.
• Thermal expansion: temperature rise $\Delta T$ elongates the optical path by $\alpha_L L \Delta T$, where $\alpha_L$ is the linear thermal-expansion coefficient.

In pump–probe settings, the time-evolving phase shift $\Delta\phi(t)$ after an impulsive excitation decomposes into ultrafast (electronic and vibrational) refractive-index changes, coherent acoustic oscillations (GHz–THz frequency, from stress wave launching), and slow thermal diffusion on nanosecond to microsecond timescales (Lockand et al., 1 Aug 2025, Zhang et al., 2018). For micro/nano-mechanical systems, vibrational excitation modulates out-of-plane displacements on sub-micrometer scales, encoded in $\phi(x, y, t)$ (Schnell et al., 2019).

Interferometric detection—inline or off-axis—captures the instantaneous optical phase, and, by repeating measurements as a function of pump–probe delay or by time-multiplexed acquisition, reconstructs a full three-dimensional dataset $\phi(x, y, t)$.

2. Instrumental Architectures and Experimental Realizations

Multiple architectures realize transient phase microscopy, each suited to specific sample classes and temporal regimes.

A. Synthetic Holographic Confocal Transient Microscopy

• Off-axis synthetic holography with a slowly translated piezo-driven reference mirror during a confocal raster scan; the spatial carrier wave encodes phase robustly across each scan line.
• Heterodyne detection via a fast photodiode enables bandwidths up to detector and digitizer limits (currently ~10 MHz, prospects for 100 GHz).
• Temporal demultiplexing (e.g., 100 ns resolution over millisecond windows) is achieved by synchronizing mechanical excitation and recasting the time axis post-acquisition (Schnell et al., 2019).

B. Widefield Phototransient Holography

• Ultrafast IR pump and femtosecond visible probe pulses interrogate the sample in widefield transmission, with off-axis holography reconstructing amplitude and phase per frame.
• Detection is performed on a high-speed CMOS camera at 1 kHz; phase images are extracted by comparing “hot” (pump on) and “cold” (pump off) frames.
• Temporal resolution is governed by probe pulse duration (1.5 ps demonstrated), with delay scanning up to tens of nanoseconds (Lockand et al., 1 Aug 2025).

C. Pump–Probe Phase-Sensitive Imaging: Bond-Selective Modalities

• BSTP (Bond-Selective Transient Phase) microscopes use pulsed IR absorption to induce bond-resonant thermal phase shifts measured by diffraction phase microscopy with ns-coherent visible probe bursts (Zhang et al., 2018).
• Synchronization electronics manage pump/probe delay (down to 70 ns pulses, MHz frame rates achievable).

D. Light Field/Defocus-Based Real-Time Phase Imaging

• Spatial and angular (4D) sampling of the light field using a microlens array allows computational synthetic refocusing, generating defocused images $I(x, y; \pm \Delta z)$ for instantaneous evaluation of the transport-of-intensity equation (TIE) via FFT (Davis, 2012). This yields quantitative phase maps at high temporal throughput (limited by camera frame rate).

E. Galvanometer-Scanning Transient Phase Microscopy

• Common-path birefringent interferometry with balanced detection, implemented in a raster-scanned (galvo mirror) platform with the flexibility for amplitude or phase readout by waveplate rotation (Coleal et al., 7 Nov 2025). Phase sensitivity is sub-mrad for single shot; sensitivity limited by polarization aberrations and “galvo phase” backgrounds.

3. Signal Processing, Phase Retrieval, and Temporal Analysis

Signal processing pipelines vary by architecture but universally involve:

• Field reconstruction: Off-axis holography involves FFT-based isolation of the +$k_r$ spatial carrier, windowing in Fourier space, and inverse transform for sample field $E_S(x, y, t)$. Phase is extracted as $\theta(x, y, t) = \arg[E_S(x, y, t)]$ (Schnell et al., 2019).
• Demodulation & referencing: Hot–cold differential phase computation, or balanced detection in interferometers, suppresses common-mode noise and static backgrounds.
• Temporal demultiplexing: For repetitive excitations, detector outputs are re-binned into time bins relative to excitation timing (e.g., $N_t = 20{,}000$ frames at 100 ns resolution) (Schnell et al., 2019).
• Spectral analysis: Time traces at each pixel are Fourier transformed, yielding vibration or acoustic mode maps $\mathcal F[h(x, y, t)] \to H(x, y, f)$ and associated phase information (Schnell et al., 2019, Lockand et al., 1 Aug 2025).
• Fast inversion: For TIE-based phase retrieval, Poisson’s equation is solved in the Fourier domain $$\Phi(k_x, k_y) = \frac{k_0}{I_0}\,\frac{G(k_x, k_y)}{k_x^2 + k_y^2}$$, ensuring regularization and zero-mean conditions (Davis, 2012).

4. Applications: Materials, Biological Imaging, and Chemical Specificity

A. Micro/nanomechanical modes: Confocal synthetic holography visualizes out-of-plane vibration modes in MEMS, AFM cantilevers, and photonic devices, with vertical sensitivity down to 5 pm RMS and lateral resolution to ~500 nm (Schnell et al., 2019).

B. Ultrafast photothermal and photoacoustic dynamics: Widefield phototransient holography resolves refractive and elastic responses from picoseconds (electronic/TOE) through nanoseconds (acoustic ringdown) to the thermal steady state. This is employed for both single-particle mechanics (e.g., polystyrene beads, $f \sim 0.2$ to $2$ GHz) and biological samples, directly decoupling TOE and expansion dynamics (Lockand et al., 1 Aug 2025).

C. Molecular/bond-selective phase imaging: BSTP microscopy provides widefield, rapid, and chemically specific label-free imaging—mapping IR absorption at submicron resolution ($\sim$500 nm), temporal resolution $\sim$70 ns, and high spectral fidelity. Applications include direct phase-resolved vibrational fingerprinting in live cells, interfaces, or microfluidic flows (Zhang et al., 2018).

D. Plunge-freeze transient-state electron microscopy: For non-optical phase mapping, plunge-freezing photoexcited specimens (e.g., mixed-halide perovskites) enables subsequent 4D-STEM and EELS mapping to visualize nanoscale transient compositional and strain phase segregation with $\sim$10 nm spatial resolution, crucial for elucidating photoinduced processes in photovoltaics (Fan et al., 17 Dec 2024).

E. Real-time dynamics in biological and medical specimens: Galvanometer-scanned TΦM permits live imaging of ultrafast refractive index changes in cells (e.g., red blood cells, hemoglobin) and fast material processes (e.g. graphene monolayers), with phase/amplitude switching for complementary contrast (Coleal et al., 7 Nov 2025).

5. Performance Metrics, Resolution, and Limitations

Modality	Spatial Resolution	Temporal Resolution	Phase Sensitivity
Confocal SOH	~500 nm–1.1 μm	100 ns (10 MHz); ps possible	5 pm RMS (230 fm/√Hz)
Widefield Holog.	~600 nm	1.5 ps–10 ns	Few μrad (single shot)
BSTP	<500 nm	70 ns (probe pulse)	mrad scale
Galvo TΦM	1–2 μm	350 fs (pulses)	10⁻²–10⁻¹ rad (exp.), sub-mrad possible
Light field TIE	0.61λ/NA (degraded by microlens pitch)	ms (camera), real time	10–100 mrad

• Sensitivity is set by phase noise (detector, shot noise, mechanical/electronic stability).
• Temporal resolution is fundamentally limited by the probe or detector bandwidth; with state-of-the-art hardware, picosecond or even sub-picosecond resolution is achievable.
• Trade-offs exist between spatial and angular (light field) sampling, or between probe fluence and sample heating/signal-to-noise (Zhang et al., 2018, Davis, 2012).
• Optical and instrumental artifacts (e.g., “galvo phase” from scanning, polarization aberrations from dichroic elements, sample birefringence) can impose significant backgrounds, correctable via design (descan) or post-processing (Coleal et al., 7 Nov 2025).
• For dynamic AFM studies, the phase response is dictated by cantilever transfer functions $H(s)$, with ring-down times $\tau = 2Q/\omega_0$, and the phase transient following a force perturbation is low-pass filtered with time constant $1/\omega_c$ (Wagner, 2018).

6. Current Challenges and Prospects

Transient phase microscopy is approaching fundamental (shot-noise) phase sensitivity and is increasingly limited by hardware: detector rise time, digitizer bandwidth, and camera frame rates. Paths to further improvement include:

• Higher-bandwidth photodetectors and digitizers (>>10 GHz) for sub-100 ps temporal resolution (Schnell et al., 2019, Lockand et al., 1 Aug 2025).
• Faster scanning/multiplexed illumination and rapid demultiplexing for real-time phase-volume acquisition (Davis, 2012).
• Automated multi-region scanning and robust software pipelines for high-throughput applications in biological and materials imaging.
• Extension to reflectance and opaque systems via non-transmission interferometry (Coleal et al., 7 Nov 2025).
• Pulse shaping or multi-wavelength strategies to decouple refractive, absorptive, and structural phase contributions.
• Advanced thermal-mechanical modeling for decoupled extraction of $\mathrm{dn/dT}$, $\alpha_L$, local heat capacity, and conductivity (Lockand et al., 1 Aug 2025).
• Application to all-optical stiffness mapping and acoustic super-resolution using GHz–THz pressure-wave modes.

Limitations remain in capturing true molecular selectivity due to cancellation of thermo-optic and expansion terms, especially in samples with compensating coefficients; further, spectral coverage is bounded by available pump lasers (Zhang et al., 2018). In widefield or scanning implementations, aberration control and efficient, stable referencing are central to achieving routine quantitative phase fidelity.

7. Significance and Outlook

Transient phase microscopy establishes a direct, quantitative probe of ultrafast structural, thermal, and chemical processes in matter, uniquely providing label-free, high-throughput maps of dynamics at nanometric spatial and femtosecond-to-microsecond temporal scales. By integrating novel optical designs, ultrafast detection, and computational inference, this approach now addresses key demands in materials science (phonon–polaron coupling, phase-change physics, microelectromechanical resonances), photonics (near-field chemical imaging), and biology (membrane mechanics, label-free cytodynamics).

Ongoing developments—improved hardware, refined analytic frameworks, and broader spectral coverage—will further extend the scope of transient phase microscopy for chemical mapping, nanomechanical metrology, dynamic phenomena in condensed matter, and super-resolved, non-destructive imaging of biological phenomena. The principal axes of progress are expected along the vectors of higher multiplexed throughput, robust quantitative phase extraction in diverse environments, and specific, model-based deconvolution of overlapping physical contributions to the measured transients.