Sapphire

The diffuser and the diffractive layer used for the experimental demonstration were fabricated using a 3D printer (Pr 110, CADworks3D). The 3D printing material we used in the experiments has wavelength-dependent absorption. Therefore, additional neuron height-dependent amplitude modulations were applied to the incident light, which can be formulated as $\begin{array}{c}\hfill a^l\left(x_i,y_i,z_i,\lambda \right)=\exp \left(-\frac{2\pi \kappa \left(\lambda \right)h_i^l}{\lambda }\right)\hfill \end{array}$ where $\kappa \left(\lambda \right)$ is the extinction coefficient of the diffractive layer material, corresponding to the imaginary part of the complex-valued refractive index $\tilde{n}\left(\lambda \right)$ , i.e., $\tilde{n}\left(\lambda \right)=n\left(\lambda \right)+j\kappa \left(\lambda \right)$ .
For the single-layer single-pixel diffractive model used for the experimental demonstration (Fig. 7), the diffractive layer consists of 120 × 120 diffractive neurons, each with a lateral size of 0.4 mm. The axial separation between any two consecutive planes was set to d = 20 mm. To compensate for the nonideal wavefront generated by the THz emitter, a square input aperture with a size of 8 × 8 mm² was used as an entrance pupil to illuminate the input object, placed 20 mm away from it. The diffraction of this aperture was also included in the forward propagation model. The size of the input objects was designed as 20 × 20 mm² (50 × 50 pixels). After being distorted by the random diffuser and modulated by the diffractive layer, the spectral power at the center region (2.4 × 2.4 mm²) of the output plane was measured to determine the class score.
To overcome potential mechanical misalignments during the experimental testing, the network was “vaccinated” with deliberate random displacements during the training stage^{53 (link)}. Specifically, a random lateral displacement $\left(D_x,D_y\right)$ was added to the diffractive layer, where $D_x$ and $D_y$ were randomly and independently sampled, i.e., $\begin{array}{c}\hfill D_x~\mathbf{U}\left(-0.4\mathrm{mm},0.4\mathrm{mm}\right),D_y~\mathbf{U}\left(-0.4\mathrm{mm},0.4\mathrm{mm}\right)\hfill \end{array}$ where $D_x$ and $D_y$ are not necessarily equal to each other in each misalignment step.
A random axial displacement $D_z$ was also added to the axial separations between any two consecutive planes. Accordingly, the axial distance between any two consecutive planes was set to $d\pm D_z=$ 20 mm $\pm D_z$ , where $D_z$ was randomly sampled as, $\begin{array}{c}\hfill D_z~\mathbf{U}\left(-0.2\mathrm{mm},0.2\mathrm{mm}\right)\hfill \end{array}$
In our experiments, we also measured the power spectrum of the pulsed terahertz source with only the input and output apertures present, which served as an experimental reference spectrum, $I_{ref}\left(\lambda \right)$ . Based on this, the experimentally measured power spectrum at the output single-pixel aperture of a diffractive network can be written as: $\begin{array}{c}\hfill s_{i,calibrated}=\frac{s_{i,measured}}{I_{ref}\left({\lambda }_i\right)}\hfill \end{array}$
The binary objects and apertures were all 3D-printed (Form 3B, Formlabs) and coated with aluminum foil to define the transmission areas. Apertures, objects, the diffuser, and the diffractive layer were assembled using a 3D-printed holder (Objet30 Pro, Stratasys). The setup of the THz-TDS system is illustrated in Fig. 7a. A Ti:Sapphire laser (Mira-HP, Coherent) generates optical pulses with a 135-fs pulse width and a 76-MHz repetition rate at a center wavelength of 800 nm, which pumps both a high-power plasmonic photoconductive terahertz source^{57 (link)} and a high-sensitivity plasmonic photoconductive terahertz detector^{58 (link)}. The terahertz radiation generated by the terahertz source is collimated by a 90° off-axis parabolic mirror and illuminates the test object. After interacting with the object, the diffuser, and the diffractive neural network, the radiation is coherently detected by the terahertz detector (single-pixel). A transimpedance amplifier (DHPCA-100, Femto) converts the current signal to a voltage signal, which is then measured by a lock-in amplifier (MFLI, Zurich Instruments). By varying the optical delay between the terahertz radiation and the optical probe beam on the terahertz detector, the terahertz time-domain signal can be obtained. By taking the Fourier transform of the time-domain signal, the spectral intensity signal is revealed to calculate the class scores for each classification/inference. For each measurement, 10 time-domain traces are collected and averaged. This THz-TDS system provides a signal-to-noise ratio larger than 90 dB and a detection bandwidth larger than 4 THz.

Cells were all positioned in the same focal plan in between an agar pad (1%) and a coverslip to be imaged in TIRF microscopy. Coverslips were cleaned by 60 min sonication in saturated KOH solution followed by two washing steps (15 min sonication in milli-Q water). Single-particle tracking of GFP-PBP1b was performed with a custom-designed fluorescence microscope based on an ASI Rapid Automated Modular Microscope System, equipped with a 100× TIRF objective (Apo TIRF, 100×, NA 1.49, Nikon), Coherent Sapphire 488–200 laser, and a dichroic beamsplitter (Di03-R488/561-t3-25 × 36, Semrock). Excitation was controlled with an acousto-optic tunable filter (AA Optoelectronics) through an Arduino (15 ms light exposure per frame). Images were acquired using an Andor iXon Ultra EMCCD camera with an effective pixel size of 130 nm. Image acquisition was supervised with MicroManager.
Tracks were built from movies using TrackMate with LoG peak detection (estimated blob diameter of 0.5 µm, quality threshold of 15, with subpixel localization). Then, peaks were linked into tracks using the “Simple LAP Tracker” (max distances of 0.4 µm, and “gap” of 2).
Data analysis with ExTrack was restricted to tracks with at least three positions. For the longest tracks, only the first 50 positions were analyzed.