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Simple, High Dynamic Range, And Efficient Extraction Of Phase Map (SHEEP) For Point Source Atom Interferometry


Atom interferometer gyroscopes use cold atoms and a series of laser pulses to measure the acceleration and rotation of a moving system and therefore can be used for inertial navigation. Some atom interferometers make measurements by imaging the atoms onto a CCD. Analyzing the atom spatial pattern typically requires advanced data processing, which is slow and can fail. Our invention introduces a new method to obtain and analyze such data by taking a series of four phase-shifted images. Each CCD pixel value is used to directly calculate gyroscope phase to measure rotation and acceleration, without the need for fitting. We call this method Simple, High dynamic range, and Efficient Extraction of Phase map (SHEEP) to highlight its strengths.

patent description

The invention, Simple, High dynamic range, and Efficient Extraction of Phase map (SHEEP), is a technique we developed to directly measure the atom phase gradient pattern in a point source matter-wave atom interferometer gyroscope. This has a number of advantages over previous methods [cite?], including the ability to measure smaller rotation rates, data processing that does not require fitting a 2D sine function to a data image, a higher measurement bandwidth, a reliable measurement with low contrast fringes, and an unambiguous rotation measurement. It is a simple and powerful method that is advantageous for an inertial navigation system.

The invention uniquely uses a set of four phase-shifted images to directly calculate the spatially-dependent atom phase map for measurements of rotation and acceleration. For each image, the laser phase is shifted such that the set of images advances through a full 360 degrees of phase, tracing out the physically-required sinusoidal variation in the atom population corresponding to the intensity at each pixel on the CCD camera. The technique traces out the sine wave while taking the data and therefore the data does not need to be fit to a sine wave in post-processing. Instead, the atom population for each of the four images is used to calculate the phase map (and from that, the rotation and acceleration) by simply subtracting the pixel values from each other and taking the arctangent of their ratio.

This technique significantly simplifies the data acquisition, processing, and analysis. That the fringe images become rotation values using a calculation, not a fitting routine, is extremely advantageous for measuring rotations that are so small that a full fringe period is not visible across the atom cloud; such low rotations are otherwise not measurable without large errors through curve fitting to image fringes. This also increases processing speed and allows fringe patterns to be easily analyzed within a nonuniform cloud envelope or low fringe contrast, all of which are important in a real-time deployed navigation device.

The phase shifting is accomplished technically by adjusting the laser frequency scan rate using common laboratory equipment, including a frequency synthesizer and electro-optic modulator. Precise control of this laser scan rate is critical for the SHEEP technique in order to reconstruct an accurate phase map.

Created September 7, 2022, Updated November 8, 2023