Quantum holography with undetected light

Abstract

Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.

Fig. 1.. Classical and quantum holography.

(A) In classical holography, the spatially dependent interference pattern of two coherent beams, the reference beam and the object beam, after interaction with the object, are recorded and used to construct the hologram of the object. (B) In our quantum holography scheme, we make use of two-photon states that can be generated by SPDC in one of two sources. The spatial shape of the object, which is transferred to the spatial shape of the light reflected/transmitted from the object, is contained in the probability amplitudes corresponding to the paired photons being generated in either of two SPDC sources.

Fig. 2.. Experimental setup for holography with undetected light.

Laser light (purple) pumps the nonlinear crystal (ppKTP) bidirectionally (beam paths a and d). It generates signal (red) and idler (green) beams either in the forward direction (beam paths b and c) or backward direction (beam paths e and f). Dichroic mirrors DM1 to DM3 separate the different beam paths. Idler light will illuminate the object (beam path c), while its hologram will be detected on the scientific complementary metal-oxide semiconductor (sCMOS) camera with the signal light (beam path e). The mirrors M1 to M3 are the interferometer end mirrors. M2 is mounted on a piezo stage to precisely move the mirror in one direction. Lenses L1 to L5 form the imaging system with the focal distances of 150 mm (L1, L2, and L3), 100 mm (L4), and 125 mm (L5).

Fig. 3.. Hologram with undetected light of a resolution target.

(A) Wide-field holographic image (using 12 frames) of the miniaturized resolution target, with a phase step of 0.82π (at the illumination wavelength). The elements contained in the yellow marked areas are the ones analyzed to determine the resolution of the setup (see Table 1). The red rectangle highlights the area used to verify the phase step of the object. (B) Phase step plot of the object, which matches with the manufactured 0.82π value.

Fig. 4.. Phase accuracy.

(A) Images of the same structure for different acquisition times of the camera and different number M of images used for the phase-shifting holography. (B) Calculated phase steps. Each point is an average of 15 image sets. The black dashed lines are the expected results. The color is in relation to the amount of images used (see legend). The cross markers refer to a sample with a step size of 0.62π, and the bullet markers refer to a sample with 0.82π step.

Fig. 5.. Amplitude accuracy.

(A) Modulation image of a 0.82π phase step mask without OD filters. (B) Modulation image of the same mask fully covered with an OD filter (OD 0.4). (C) Relative modulation calculated values for the three different areas marked in the correspondent colors in (A) and expected transmission (black solid line) for different object transmission values, experimentally implemented by placing different OD filters in front of the phase mask. The modulation values are retrieved from holographic images with M = 12 phase steps each with 500-ms exposure time. ROI, region of interest.

Fig. 6.. Exemplary raw image set.

One set of recorded images for the phase-shifting holography calculation ordered from left to right and top to bottom. (A) The object images. (B) The reference images.