Images hidden in noise revealed by quantum-inspired phase imaging method

Researchers from the Faculty of Physics at the University of Warsaw, together with colleagues from Stanford University and Oklahoma State University, have introduced a quantum-inspired phase imaging method based on light intensity correlation measurements robust to phase noise.

The new imaging method can work even in extremely low illumination and may prove useful in emerging applications such as infrared and X-ray interferometric imaging and quantum and matter wave interferometry. The research results were published in Scientists progress.

It doesn’t matter if you take photos of a cat with your smartphone or image cell cultures with an advanced microscope, you do so by measuring the intensity (brightness) of light pixel by pixel. Light is characterized not only by its intensity but also by its phase. Interestingly, transparent objects can become visible if you can measure the phase delay of the light they introduce.

Phase contrast microscopy, for which Frits Zernike received a Nobel Prize in 1953, revolutionized biomedical imaging with the possibility of obtaining high-resolution images of various transparent and optically thin samples. The research area born from Zernike’s discovery includes modern imaging techniques such as digital holography and quantitative phase imaging.

“It enables label-free, quantitative characterization of living samples, such as cell cultures, and may find applications in neurobiology or cancer research,” explains Dr. Radek Lapkiewicz, director of the Quantum Imaging Laboratory at the Faculty of Physics of the University of Warsaw.

However, improvements are still possible. “For example, interferometry, a standard measurement method for precise thickness measurements at any point on the object being examined, only works when the system is stable, not subject to shock or disturbance. It is very difficult to carry out such a test, because for example, in a moving car or on a shaking table”, explains Jerzy Szuniewcz, doctoral student at the Faculty of Physics at the University of Warsaw.

Researchers from the Faculty of Physics at the University of Warsaw, together with colleagues from Stanford University and Oklahoma State University, decided to tackle this problem and develop a new phase imaging method insensitive to phase instability.

Back to the old school

How did the researchers come up with the idea for this new technique? Already in the 1960s, Leonard Mandel and his group demonstrated that even when the intensity of an interference is not detectable, correlations can reveal its presence. “Inspired by Mandel’s classic experiments, we wanted to investigate how intensity correlation measurements could be used for phase imaging,” says Lapkiewicz.

In a correlation measurement, they looked at pairs of pixels and observed whether they became lighter or darker at the same time.

“We showed that such measurements contain additional information that cannot be obtained using a single photo, i.e. measuring intensity. Using this fact, we demonstrated that in interference-based phase microscopy, observations are possible even when standard interferograms average the total loss of phase information and no fringes are recorded in the intensity.

“With a standard approach, one might assume that there is no useful information in such an image. However, it turns out that the information is hidden in the correlations and can be recovered by analyzing several independent photos of an object that allows you to obtain a perfect image of interferograms, even if ordinary interference is undetectable because of the noise,” adds Lapkiewicz.

“In our experiment, light passing through a phase object (our target, which we want to study) is superimposed on a reference light. A random phase delay is introduced between the object and the reference light beams. This delay phase simulates a disturbance. obstructing standard phase imaging methods. Therefore, no interference is observed when the intensity is measured, i.e. no information about the phase object can be obtained from intensity measurements.

“However, the spatially dependent intensity-intensity correlation displays a fringe pattern that contains the complete information about the phase object. This intensity-intensity correlation is not affected by any temporal phase noise varying more slowly than the speed of the detector (~10 nanoseconds in time. experiment performed) and can be measured by accumulating data over an arbitrarily long period of time – a game changer – a longer measurement means more photons, which results in a greater precision,” explains Jerzy Szuniewicz, the first author of the work.

Simply put, if we were to record a single frame of film, that single frame would not give us any useful information about the appearance of the object under study. “Therefore, we first recorded a whole series of these images using a camera, then multiplied the measurement values ​​at each pair of points in each image. We averaged these correlations and recorded a complete image of our object,” explains Szuniewicz.

“There are many possible ways to recover the phase profile of an observed object from a sequence of images. However, we have proven that our method based on an intensity-intensity correlation and a technique called holography off-axis allows for optimal reconstruction accuracy.” » says Stanisław Kurdziałek, the second author of the article.

A bright idea for dark environments

A phase imaging approach based on intensity correlation can be widely used in very noisy environments. The new method works with both classical (laser and thermal) and quantum light. It can also be implemented in the photon counting regime, for example using single photon avalanche diodes. “We can use it in cases where there is little light available or when we cannot use high light intensity so as not to damage the object, for example a delicate biological sample or a work of art,” Szuniewicz explains.

“Our technique will broaden prospects in the field of phase measurements, including emerging applications such as infrared and X-ray imaging and quantum and matter wave interferometry,” concludes Lapkiewicz.