Many powerful imaging techniques for cold atoms are based on determining the optical density by comparing a beam image having passed through the atom cloud to a reference image taken under similar conditions with no atoms. In practice, the beam profile typically contains interference fringes whose phase is not stable between camera exposures. To reduce the error of these fringes in the computed optical density, an algorithm based on principle component analysis (PCA) is often employed. However, PCA is general purpose and not tailored to the specific case of interference fringes. Here we demonstrate an algorithm that takes advantage of the Fourier space structure of interference fringes to further reduce the residual fringe signatures in the optical density.
Many powerful imaging techniques for cold atoms are based on determining the optical density by comparing a beam image having passed through the atom cloud to a reference image taken under similar conditions with no atoms. In practice, the beam profile typically contains interference fringes whose phase is not stable between camera exposures. To reduce the error of these fringes in the computed optical density, an algorithm based on principle component analysis (PCA) is often employed. However, PCA is general purpose and not tailored to the specific case of interference fringes. Here we demonstrate an algorithm that takes advantage of the Fourier space structure of interference fringes to further reduce the residual fringe signatures in the optical density.
Absorption imaging is the foundation for quantitative measurements in experiments on ultracold atoms. This technique mainly involves capturing images of both the probing light field and the atom absorption light field. In this process, the unavoidable jitter of the probing light introduces imaging noise of fringe patterns into the atomic optical density distribution OD. In conventional fringe removal algorithms, this type of noise can be normalized by constructing an optimal reference image from multiple reference images that have been actually taken, which shares similar fringe patterns to an absorption image (Fig. (a)). Although this method works well in the region without atomic signal, they often overlook the modulation of the noise signal due to atomic absorption effects, leading to persistent residual fringes on the atom clouds. This problem becomes more pronounced with atomic density increasing. Here, we propose an enhanced fringe removal algorithm that takes into account the effects of atomic absorption, and actively modulates the intensity of the noise signal in the reference image constructed by conventional fringe removal algorithms (Fig. (b)), effectively preventing the residual fringes from forming, thus significantly improving the signal-to-noise ratio of the atomic images. When applied to the absorption imaging of homogeneous Fermi gases with high density, as shown in Fig. (d), this new algorithm successfully reduces the relative standard deviation of optical depth characterizing atomic density fluctuations by approximately 37%, which is about 3 times the relative standard deviation by conventional algorithm. Three subgraphs in Fig. (e) show the optical depth distribution at corresponding data points labeled by square boxes in Fig. (d). Furthermore, we also use this technique to quantitatively determine the second sound in the unitary Fermi superfluid of 6Li atoms. Compared with conventional fringe removal methods, our new algorithm increases the correlation function’s contrast of the density wave nearly 4 times, therefore enhancing the intensity of the density response spectrum by approximately 15% with half the measured standard error, paving the way for quantitatively determining the speed and attenuation of the second sound. These results demonstrate that the enhanced fringe removal algorithm not only effectively suppresses fringe noise, but also facilitates the identification and detection of important physical phenomena in high-density atomic systems, such as some collective excitations and new quantum phases.
Absorption imaging is a widely employed technique for detecting cold atom clouds and Bose-Einstein condensates (BECs). There are situations where such images may suffer from unwanted interference fringes, resulting in uncertainties in determining crucial parameters such as the atom number, temperatures, or even dynamics in small timescales. Reducing the acoustic vibrations and recording image frames synchronized with the source of such vibrations can largely reduce these fringes; however, some residual fringes still need to be taken care of for precision measurements. In this study, we propose an efficient image post-processing technique for noise reduction that effectively mitigates such interference patterns. Our approach makes use of the well-known eigenface recognition algorithm, combined with an optimized masking strategy applied to the image of the atomic cloud using a small number of basis sets. The use of a limited basis set ensures minimal computational time, allowing this method to be readily incorporated into every experimental run. Through the application of our technique, we successfully reduce interference fringes and improve the accuracy of parameter estimation by 50% in the absorption imaging of cold atoms. The temperature uncertainties of cold 87 Rb atoms are reduced by more than 50% after the algorithm is applied. This approach holds significant promise for enhancing the reliability and precision of experimental measurements in diverse research fields where absorption imaging is employed.
Optical absorption imaging is a basic detection technique for obtaining information from matter waves, in which the absorption signal can be obtained by comparing the recorded detection light field with the light field in the presence of absorption, thereby giving the spatial distribution of the atoms. The noise in detection arises mainly from differences between the two recorded light field distributions, which is difficult to avoid in experiments. In this work, we present an optimized fringe removal algorithm, developing a method to generate an ideal reference light field, avoiding the noise generated by the light field difference, and suppressing the noise signal to the theoretical limit. Using principal component analysis, we explore the optimal calculation area and how to remove noise information from the basis to allow optimal performance and speed. As an example, we consider scattering atomic peaks with a small number of atoms in a triangular lattice. Compared with the conventional processing method, our algorithm can reduce the measured atomic temperature variance by more than three times, giving a more reliable result.
Eigenface method used in face recognition is introduced to reduce the pattern of interference fringes appearing in the absorption image of cold rubidium atom cloud trapped by an atom chip. The standard method for processing the absorption image is proposed, and the origin of the interference fringes is analyzed. Compared with the standard processing method which uses only one reference image, we take advantage of fifty reference images and reconstruct a new reference image which is more similar to the absorption image than all of the fifty original reference images. Then obvious reduction of interference fringes can be obtained.
When the initial size of an atom cloud in a cold atom interferometer is negligible compared to its size after free expansion, the interferometer is approximated to a point-source interferometer and is sensitive to rotational movements by introducing an additional phase shear in the interference sequence. This sensitivity on rotation enables a vertical atom-fountain interferometer to measure angular velocity in addition to gravitational acceleration, which it is conventionally used to measure. The accuracy and precision of the angular velocity measurement depends on proper extraction of frequency and phase from spatial interference patterns detected via the imaging of the atom cloud, which is usually affected by various systematic biases and noise. To improve the measurement, a pre-fitting process based on principal component analysis is applied to the recorded raw images. The contrast of interference patterns are enhanced by 7-12 dB when the processing is present, which leads to an enhancement in the precision of angular velocity measurements from 6.3 μrad/s to 3.3 μrad/s. This technique is applicable in various instruments that involve precise extraction of frequency and phase from a spatial interference pattern.
High-sensitivity imaging of ultracold atoms is often challenging when interference patterns are imprinted on the imaging light. Such image noises result in low signal-to-noise ratio and limit the capability of extracting subtle physical quantities. Here we demonstrate an advanced fringe removal algorithm for absorption imaging of ultracold atoms, which efficiently suppresses unwanted fringe patterns using a small number of sample images without taking additional reference images. The protocol is based on an image decomposition and projection method with an extended image basis. We apply this scheme to raw absorption images of degenerate Fermi gases for the measurement of atomic density fluctuations and temperatures. A quantitative analysis shows that image noises can be efficiently removed with only tens of reference images, which manifests the efficiency of our protocol. Our algorithm would be of particular interest for quantum emulation experiments in which several physical parameters need to be scanned within a limited time duration.