Widefield Phototransient Holography

• Widefield phototransient holography is a phase-sensitive imaging method that combines pump–probe techniques with off-axis digital holography to capture transient complex field changes.
• It utilizes two-dimensional interferometric phase retrieval and temporal encoding to achieve nanoscale precision across extended fields of view.
• Applications span nanoparticle tracking, mid-infrared photothermal imaging, and quantitative analysis of thermo-optic and thermo-elastic properties.

Widefield phototransient holography is a phase-sensitive pump–probe imaging framework that combines widefield optical microscopy with off-axis digital holography to record pump-induced transient changes in transmitted or scattered probe fields across an extended field of view. In the nanoparticle-tracking literature it is also described as ultrafast holographic transient microscopy, and in mid-infrared photothermal implementations it phase-resolves optical responses from pico- to tens of nanoseconds following vibrational overtone excitation, thereby linking non-equilibrium photoacoustic dynamics to steady-state photothermal contrast (Liebel et al., 2021, Lockand et al., 1 Aug 2025). A related temporal-imaging lineage comes from heterodyne time-lens and digital time-holography, whose proposed two-dimensional generalization explicitly formulates a route from one-dimensional temporal encoding to true widefield phototransient holography (Tikan et al., 2017).

1. Origins, scope, and conceptual lineage

The conceptual basis of widefield phototransient holography is the combination of interferometric phase retrieval with ultrafast pump–probe contrast. In heterodyne time-lens systems, a complex signal $E_s(t)$ and a reference $E_r$ are encoded on a two-dimensional camera such that the horizontal axis maps time and the vertical axis maps interferometric phase. In that setting, direct amplitude-and-phase recording was demonstrated with $\Delta t \approx 200\,\mathrm{fs}$ in heterodyne time-lens mode and $\Delta t \approx 80\,\mathrm{fs}$ in digital temporal holography, over a temporal field of view of approximately $40\,\mathrm{ps}$ (Tikan et al., 2017).

That same work proposed an explicit extension from one-dimensional temporal holography to a widefield modality. The proposal replaces the pointwise input $E_s(t)$ by a two-dimensional object field $E_s(x,y,t)$, introduces a two-dimensional time lens, and reconstructs the object by two-dimensional Fourier filtering followed by cascaded angular-spectrum propagation,

$$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$

In that formulation, widefield phototransient holography is not merely widefield imaging plus pump–probe timing; it is a full complex-field measurement architecture intended to recover $E_s(x,y,t)$ rather than intensity alone (Tikan et al., 2017).

Realized microscope implementations have followed two complementary directions. One direction uses transient changes in nanoparticle scattering to enable background-free identification, digital refocusing, and three-dimensional tracking in scattering environments. The other uses mid-infrared vibrational excitation and visible-light phase readout to disentangle thermo-optic, thermo-elastic, and acoustic contributions in photothermal microscopy. Together, these directions define the present scope of widefield phototransient holography as a family of phase-sensitive, widefield, ultrafast holographic methods.

2. Instrumental configurations and pump–probe timing

In ultrafast holographic transient microscopy for nanoparticle imaging, a femtosecond probe pulse at $550$–$E_r$0 is launched into a wide-field dark-field or bright-field microscope with $E_r$1 and imaged onto a CMOS camera at $E_r$2 magnification. Scattered or transmitted light from the sample interferes with two reference beams generated by a two-dimensional $E_r$3–$E_r$4 phase grating with $E_r$5 grooves/mm conjugate to the camera. The pump is a $E_r$6 pulse derived as the second harmonic of a $E_r$7, $E_r$8 Ti:Sapphire amplifier, made co-linear and co-focal with the probe. Its diameter is approximately $E_r$9 at $\Delta t \approx 200\,\mathrm{fs}$0, large enough to uniformly illuminate a $\Delta t \approx 200\,\mathrm{fs}$1 field of view. Two synchronized choppers modulate the pump and the two reference arms in anti-phase so that pump-ON and pump-OFF holograms are multiplexed within a single $\Delta t \approx 200\,\mathrm{fs}$2 camera exposure (Liebel et al., 2021).

In mid-infrared photothermal widefield phototransient holography, the pump is a sub-picosecond pulse of approximately $\Delta t \approx 200\,\mathrm{fs}$3 with $\Delta t \approx 200\,\mathrm{fs}$4 bandwidth, tunable from $\Delta t \approx 200\,\mathrm{fs}$5 to $\Delta t \approx 200\,\mathrm{fs}$6, generated by a home-built noncollinear OPA plus booster stage pumped at $\Delta t \approx 200\,\mathrm{fs}$7 by a Yb:KGW amplifier operating at $\Delta t \approx 200\,\mathrm{fs}$8, $\Delta t \approx 200\,\mathrm{fs}$9, and $\Delta t \approx 80\,\mathrm{fs}$0. The visible probe is a $\Delta t \approx 80\,\mathrm{fs}$1 pulse of about $\Delta t \approx 80\,\mathrm{fs}$2, chirped to $\Delta t \approx 80\,\mathrm{fs}$3 by a double-pass grating stretcher. The pump is focused into the sample plane to approximately $\Delta t \approx 80\,\mathrm{fs}$4 full width at half maximum and modulated at $\Delta t \approx 80\,\mathrm{fs}$5. Pump–probe delays up to tens of nanoseconds are obtained with a $\Delta t \approx 80\,\mathrm{fs}$6–$\Delta t \approx 80\,\mathrm{fs}$7 double-pass translation stage, while sub-$\Delta t \approx 80\,\mathrm{fs}$8 delays are controlled by a piezo stage. After a $\Delta t \approx 80\,\mathrm{fs}$9 beamsplitter generates object and reference waves, both are coupled into a home-built transmission microscope with $40\,\mathrm{ps}$0 magnification and $40\,\mathrm{ps}$1, and recombined off-axis on a $40\,\mathrm{ps}$2 CMOS camera with a reference tilt of approximately $40\,\mathrm{ps}$3–$40\,\mathrm{ps}$4 (Lockand et al., 1 Aug 2025).

A further instrumental development is a bidirectional femtosecond mid-infrared pump–probe holographic microscope that can switch between forward-scattering, backward-scattering, and internal-forward-scattering geometries in one instrument. In this system, a femtosecond $40\,\mathrm{ps}$5 probe is split $40\,\mathrm{ps}$6 into sample and reference arms, the reference delay is motorized, and the beams interfere off-axis on a CMOS sensor. Forward scattering uses two-sided access, backward scattering uses single-sided access via a flip-mount, and internal forward scattering uses the back-reflection from the top surface of a mid-infrared-transparent substrate as an internally generated illumination wave. A second motorized delay line scans the pump–probe delay from $40\,\mathrm{ps}$7 to tens of nanoseconds, with a $40\,\mathrm{ps}$8 modulated mid-infrared pump and $40\,\mathrm{ps}$9 probe detection producing alternating hot and cold holograms (Robertson et al., 3 Jul 2026).

3. Signal formation and transient phase physics

The fundamental holographic signal model is the interference of a stable reference field with a pump-sensitive signal field. In scattering-based implementations,

$E_s(t)$0

and the recorded hologram is

$E_s(t)$1

Because the pump-induced perturbation appears only in the signal field, subtraction of pump-ON and pump-OFF channels yields a differential hologram

$E_s(t)$2

which suppresses static background scattering (Liebel et al., 2021).

In mid-infrared photothermal implementations, the principal observable is a differential phase image,

$E_s(t)$3

The total phase shift accrued by the probe after traversing a heated sample of thickness $E_s(t)$4 is written as the sum of thermo-optic and thermo-elastic terms,

$E_s(t)$5

Under homogeneous heating,

$E_s(t)$6

while linear expansion gives

$E_s(t)$7

Typical values given for polystyrene are $E_s(t)$8 and $E_s(t)$9 (Lockand et al., 1 Aug 2025).

The transient thermal dynamics are explicitly non-steady-state on the relevant length and time scales. Immediately after vibrational excitation, intra-molecular vibrational relaxation converts overtone absorption into heat within $E_s(x,y,t)$0 to $E_s(x,y,t)$1. The local temperature rise is approximated by

$E_s(x,y,t)$2

with $E_s(x,y,t)$3 and $E_s(x,y,t)$4 for polymers. For sub-$E_s(x,y,t)$5 beads, $E_s(x,y,t)$6, so non-steady-state conditions dominate the reported observation window. The Lorentz–Lorenz relation,

$E_s(x,y,t)$7

is used to explain the observed two-stage phase dynamics: on picosecond time scales the mean polarizability changes through temperature, whereas density evolves on nanosecond time scales through acoustic expansion (Lockand et al., 1 Aug 2025).

This phase picture aligns with the scattering-transient description used for resonant nanoparticles. There, a resonant particle absorbs the pump pulse, produces a hot-electron distribution, and heats on sub-picosecond time scales, modifying the local refractive index and absorption coefficient according to

$E_s(x,y,t)$8

which modulates the scattering amplitude as $E_s(x,y,t)$9 (Liebel et al., 2021).

4. Hologram demodulation, differential processing, and 3D reconstruction

The reconstruction pipeline in widefield phototransient holography follows standard off-axis digital holography, but it is adapted for differential pump–probe imaging. Recorded holograms

$$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$0

contain a zero-order term and $$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$1 diffraction orders. A single two-dimensional FFT isolates the $$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$2 order in reciprocal space; a circular mask around that order is inverse transformed to recover the complex field

$$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$3

In the mid-infrared implementation, a GPU-accelerated pipeline based on Mellanox $$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$4 and an A4000 GPU performs FFT, masking, and inverse FFT in real time. Residual background phase gradients from beam drift are removed by least-squares fitting of a linear phase tilt in regions free of sample, and no phase unwrapping is required within the reported $$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$5 interval because the signals remain up to approximately $$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$6 (Lockand et al., 1 Aug 2025).

In the multiplexed UHT format, the two non-collinear reference waves shift the pump-ON and pump-OFF cross-terms to distinct off-axis positions. The simplified multiplexed intensity is written as

$$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$7

A two-dimensional FFT therefore produces a central DC term and four off-axis peaks corresponding to the two cross-terms and their conjugates. Cropping each peak, removing the linear phase ramp, and inverse transforming yields separate complex fields $$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$8 and $$H(\omega,k_x,k_y)=\exp\!\bigl[i(\beta_t\omega^2+\beta_x k_x^2+\beta_y k_y^2)/2\bigr].$$9, from which the differential field $E_s(x,y,t)$0 is reconstructed (Liebel et al., 2021).

For three-dimensional localization, each recovered complex field at $E_s(x,y,t)$1 is numerically propagated using angular-spectrum backpropagation over $E_s(x,y,t)$2 in $E_s(x,y,t)$3 steps with kernel

$E_s(x,y,t)$4

where $E_s(x,y,t)$5. Candidate hotspots are then identified by three-dimensional convolution and noise thresholding, lateral positions are refined by two-dimensional Gaussian fitting, axial positions are refined by the Tamura image-sharpness metric

$E_s(x,y,t)$6

and frame-to-frame associations are linked into trajectories using the algorithm of Jaqaman et al. (Liebel et al., 2021).

5. Reported measurements and operating envelopes

In time-resolved infrared photothermal widefield phototransient holography, representative data were obtained from immobilized polystyrene spheres of diameter $E_s(x,y,t)$7, $E_s(x,y,t)$8, and $E_s(x,y,t)$9 on glass, pumped at $550$0 with fluence $550$1 and probed at $550$2 with $550$3 duration. For a $550$4 bead, the measured response shows no signal for $550$5, a coherent artifact at $550$6 with $550$7 and instrument response of about $550$8, acoustic oscillation for $550$9 with peak-to-peak amplitude $E_r$00 and resonance near $E_r$01, and a slow decay toward a thermal-diffusion-limited baseline for $E_r$02. FFT analysis gives size-dependent acoustic frequencies of approximately $E_r$03 for $E_r$04, $E_r$05 for $E_r$06, and $E_r$07 for $E_r$08, consistent with the bead fundamental mode $E_r$09 using $E_r$10. In water, $E_r$11 beads show damping in less than one full oscillation period, ring-shaped pressure waves with extracted velocity $E_r$12, and a steady-state $E_r$13 reached at $E_r$14; for $E_r$15 spheres, $E_r$16 is extrapolated. The probe diffraction limit is approximately $E_r$17, and a widefield field of view of about $E_r$18 at $E_r$19 magnification is reported, with sub-micrometer lateral resolution routinely achieved (Lockand et al., 1 Aug 2025).

In scattering-based UHT microscopy, the reported field of view is $E_r$20, with $E_r$21 integration per frame and simultaneous recording of phototransient signals during three-dimensional localization. The temporal resolution is nominally $E_r$22, although the demonstrated measurements were acquired at $E_r$23 to allow manual delay changes; with a faster camera, the all-optical lock-in scheme permits up to about $E_r$24. The lateral resolution is estimated as approximately $E_r$25 from $E_r$26 and $E_r$27, while localization precision reaches $E_r$28 laterally and $E_r$29 axially. Differential signals for $E_r$30 Au nanoparticles reach approximately $E_r$31–$E_r$32 at zero delay under fluence of about $E_r$33, whereas off-resonant latex nanoparticles remain at $E_r$34, enabling background-free discrimination. Reported examples include clean separation of $E_r$35 Au from $E_r$36 polystyrene despite identical steady-state scattering amplitudes, tracking of approximately $E_r$37 freely diffusing $E_r$38 Au nanoparticles in water over $E_r$39, and transient spectroscopy of a single $E_r$40 Au nanoparticle over $E_r$41–$E_r$42 while computationally refocused in three dimensions (Liebel et al., 2021).

These operating envelopes show that the term “widefield” has been realized in two distinct but compatible senses: widefield volumetric holographic tracking with digital refocusing, and widefield phase-resolved photothermal imaging with nanosecond delay scanning and sub-micrometer lateral resolution.

6. Detection geometries, interpretation, and emerging directions

A recurrent interpretive issue in photothermal microscopy is whether the measured phase can be read as a purely thermal observable. The reported phase-resolved measurements show instead a succession of rapid transient-induced phase shifts, coherent expansion and acoustic ringing, and later thermalisation. The three-stage description is explicit: Stage I on picosecond time scales is an instantaneous $E_r$43 contribution with $E_r$44; Stage II from picoseconds to nanoseconds is dominated by sample expansion and acoustic oscillations with $E_r$45 around baseline; Stage III from nanoseconds to microseconds is thermal diffusion toward the steady-state photothermal value on the milliradian scale. Accordingly, the recommended strategy for quantitative mid-infrared photothermal imaging is to choose pump–probe delays near $E_r$46 but still much shorter than $E_r$47, for example $E_r$48–$E_r$49 for biological particles smaller than $E_r$50, in order to avoid acoustic artifacts and retain diffraction-limited resolution (Lockand et al., 1 Aug 2025).

A second practical issue is the trade-off between forward-scattering and backward-scattering detection geometries. Forward scattering provides quantitative, shape-independent phase contrast but requires two-sided optical access. Backward scattering permits single-sided access, but for micron-scale objects its signals are strongly distorted by depth-dependent interference. In the bidirectional holographic phototransient microscope, internal forward scattering addresses this trade-off by using the reflection from the top surface of the mid-infrared-transparent substrate as a delayed, internally generated forward-scattering wave. Temporal coherence gating isolates that term by matching the reference-arm delay to the longer optical path of the two-pass signal. The corresponding phase expressions are

$E_r$51

For $E_r$52 beads, forward scattering and internal forward scattering yield identical phase amplitudes and temporal dynamics, whereas backward scattering produces approximately twice the phase amplitude but also depth-dependent phase jumps and clover-leaf distortions. Under shot-noise-limited holography, the larger backward-scattering phase gives at most a $E_r$53 SNR benefit, so the higher amplitude does not imply superior quantitative fidelity (Robertson et al., 3 Jul 2026).

The future directions identified in the literature are tied directly to the phase sensitivity of the method. The reported separation of thermo-optic and expansion contributions is stated to enable quantitative extraction of $E_r$54 and $E_r$55 without ambiguity. Acoustic resonances characterized by $E_r$56 and damping $E_r$57 are proposed as a basis for all-optical stiffness measurements, with widefield time-resolved holography mapping local acoustic modes into two-dimensional stiffness images. A further proposed direction is super-resolution acoustic imaging: at gigahertz frequencies the acoustic wavelength is of order $E_r$58, whereas $E_r$59 gold nanoparticles resonating near $E_r$60 would correspond to $E_r$61. This suggests that combining ultrafast widefield phototransient holography with high-frequency acoustic transducers could enable label-free, nanometer-scale chemical mapping of biological specimens. From the time-lens perspective, a distinct but related proposal is widefield imaging of ultrafast chemical reactions, transient carrier dynamics in semiconductors, and plasma shock fronts or microfluidic flows on picosecond time scales through direct recovery of $E_r$62 (Lockand et al., 1 Aug 2025, Tikan et al., 2017).

Across these variants, widefield phototransient holography is defined less by a single instrument than by a common measurement principle: pump-induced complex-field perturbations are interferometrically encoded over a wide field, digitally separated from static background, and interpreted in time regimes where thermo-optic, thermo-elastic, and acoustic contributions can be resolved rather than conflated.