Diverse areas of research require imaging under low-light conditions to acquire information. Examples include imaging faint stars in astronomy and fluorescent proteins in single molecule microscopy, where interstellar distances and intracellular particle positions, respectively, can be determined from the resulting images. A key objective in these types of parameter estimation studies is to extract the desired quantities with the highest accuracy possible. In single molecule microscopy, the performance of the techniques for super-resolution image reconstruction1,2 and 3D particle tracking3, 4 depends on how accurately the position of a particle can be estimated.
A fundamental obstacle to high-accuracy parameter estimation from digital images is that the acquired data is a deteriorated version of the ideal image, which would be free of pixelation and detector noise. Common image acquisition devices, such as CCD or electron-multiplying CCD (EMCCD) detectors, pixelate the image and introduce measurement noise to the image during the detector's readout process. Images produced by an EMCCD detector also contain additional noise due to the stochasticity of the detector's signal amplification (i.e., electron multiplication) process, which augments weak signals to such an extent that the readout noise is rendered insignificant. Our prior work showed that pixelation and detector noise significantly affect the accuracy with which quantities of interest can be estimated from image data.5, 6 Thus, the mitigation (or ideally, the elimination) of these effects can lead to significantly improved estimation accuracies, and it is especially important for low-light imaging where the estimation accuracies are already relatively poor due to the low numbers of detected photons.3, 5
Figure 1. Standard and mesh representations of ultrahigh accuracy imaging modality (UAIM) and conventional electron-multiplying CCD (EMCCD) images of an Atto647N molecule. The mesh representation provides a clear visual contrast between the spiky appearance of the UAIM image and the relatively smooth, Gaussian-like profile of the EMCCD image. The UAIM image was acquired under conditions where an average of 191 photons per image were detected from the Atto647N molecule, and it was captured with an effective pixel size of 16nm using a 1000×magnification. A mean photon count of 0.52 was detected in its brightest pixel. The conventional EMCCD image was acquired under conditions where an average of 183 photons per image were detected from the Atto647N molecule, and it was captured with an effective pixel size of 253.97nm using a standard 63×magnification. A mean photon count of 48.13 was detected in its brightest pixel. Scale bars=0.5μm.
To address this concern, we recently introduced the ultrahigh accuracy imaging modality (UAIM),7 an imaging method that enables parameter estimations that are nearly as accurate as those that can be attained with an ideal noiseless and unpixelated detector. UAIM uses an EMCCD detector operating at a high signal amplification level (i.e., a high electron-multiplying gain setting) to acquire data in an unconventional configuration where the photon flux is typically less than one photon per pixel per exposure. We selected this atypical imaging regime based on our evidence that the signal in an EMCCD pixel is least corrupted by detector noise when it consists of less than one photon on average.6, 7
The image of a fluorescent point source acquired using UAIM has an unconventional appearance when compared to an image captured by an EMCCD detector under normal conditions where significantly more than one photon per pixel were detected (see Figure 1). Although we detected a similar number of photons from the point source in both images, the UAIM image appeared noisy, with spikes resulting from the combination of low photon flux (i.e., less than one photon/pixel) and high signal amplification of the EMCCD detector. On the other hand, the conventional EMCCD image had a smooth appearance that resembled a Gaussian profile. Despite the unusual appearance of the UAIM data, we demonstrated that when fluorescent beads and single molecules were imaged using UAIM, their positional coordinates could be determined with approximately 200% better accuracy (i.e., approximately twofold lower standard deviations) than when conventional EMCCD imaging was used.7
While UAIM can be implemented in different ways, a simple, yet powerful approach is to use very high magnification. This technique distributes the detected photons over many pixels, thereby achieving a low photon flux of less than one photon/pixel. For example, in fluorescence microscopy, instead of imaging the sample at a standard 100× magnification, one might use additional magnifiers to image at a total magnification of 1000×. We used this method to acquire the UAIM image shown in Figure 1. The high-magnification configuration produces a more finely sampled image (i.e., a higher resolution image) by reducing the effective pixel size of the detector. In this way, the high-magnification implementation not only mitigates the deteriorative effect of detector noise due to the low photon flux regime, but it also minimizes the deteriorative effect of pixelation to produce an image that more closely approximates an ideal image.
The UAIM technique represents a powerful methodology that produces images from which information can be extracted with nearly the same accuracy that is achievable only with an ideal detector, i.e., one that is devoid of pixelation and noise. The methodology can be applied to many low-light imaging applications, including fluorescence microscopy, astronomy, surveillance, and machine vision. Future work will include incorporating UAIM into other existing imaging modalities, exploring the use of UAIM in additional applications, and optimizing different aspects of UAIM, such as its data analysis component.
This research was supported in part by grants from the National Institutes of Health and from the Cancer Prevention and Research Institute of Texas.
Jerry Chao, Sripad Ram, Raimund Ober
Department of Electrical Engineering
University of Texas at Dallas
E. Sally Ward
Department of Immunology
University of Texas Southwestern Medical Center
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2. M. Heilemann, S. van de Linde, M. Schttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, M. Sauer, Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes, Angewandte Chemie Int'l. Edition 47(33), p. 6172-6176, 2008.
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4. M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, W. E. Moerner, Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function, Proc. National Academy Sci. 107(42), p. 17864-17871, 2010.
5. R. J. Ober, S. Ram, E. S. Ward, Localization accuracy in single-molecule microscopy, Biophysical J. 86(2), p. 1185-1200, 2004.
6. J. Chao, E. Ward, R. Ober, Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices, Multidimensional Syst. Signal Process. 23(3), p. 349-379, 2012.
7. J. Chao, S. Ram, E. S. Ward, R. J. Ober, Ultrahigh accuracy imaging modality for super-localization microscopy, Nat. Methods 10, p. 335-338, 2013.