Establishing the intensifier set up for detecting single photons using the electron amplification of the image intensifier (8,100×). (A) The readout noise of individual pixels of the CMOS chip used here. The map (top) of the means (left) and variances (right) of pixels (256 × 256 pixels) and their histograms (bottom; Huang et al., 2013) for 1,000 frames obtained at 10 kHz. (B) Typical images of single photons obtained as a function of the intensifier gain, using the newly developed camera system. They were obtained by amplifying single electrons emitted from the image-intensifier photocathode by the arrivals of single photons (uniform Köhler illumination by the strongly attenuated halogen lamp of the microscope). The amplifications were 506, 8,100, and 129,600 (increases by a factor of 16 from left to middle and middle to right images). Note that the term “overall electron amplification (of the camera system)” always excludes the 40% quantum efficiency of the image intensifier photocathode throughout this report, because we discuss the amplification of the number of electrons from the photoelectrons emitted by the photocathode. The range of the gray levels of the images shown here (both B and C) was set for 8 bits from 0 to 550 electrons/pixel at the CMOS sensor (from black to white). (C) As an example, we show that an overall electron amplification of 506× by the camera system would not be sufficient for the consistent detection of single photons, due to the readout noise. (C a) A schematic figure showing a 7 × 7 pixelated image for a single detected photon amplified to a total of 517 electrons (without noise and background; computer-generated, assuming an overall amplification of 506× with an SD of 0.28 ± 0.085 pixels as in B left). The number of amplified electrons in each pixel on the CMOS sensor is shown. A full well of 45,000 electrons/pixel of the CMOS sensor (SA1) is scaled to 12 bits (4,095 camera counts, and hence a unit camera count = 10.99 [≈11] electrons per pixel), and thus each number is a multiple of 11 electrons. (C b) Three arbitrarily selected (experimentally obtained) 7 × 7 pixelated images representing the spatial distributions of the readout noise of the CMOS sensor employed in this study (37-root-mean-square electrons/pixel/frame; see “Ultrahigh-speed intensified CMOS camera system: Design and operation” in Materials and methods). To detect a (photon-converted) emitted electron, its image, such as that shown in a, must be detectable in the presence of spatiotemporally varying noise, as shown here. The detectability will be enhanced by an increase of the electron amplification. See D. (D) Stochastic gain variations (fluctuations) of the image intensifier. At the level of detecting single photons, the gain variations are large (at the level of detecting single molecules, relative variations will become smaller due to averaging over all detected photons). In these histograms, the distributions of the number of total electrons stored at the CMOS sensor of the camera system for each single detected photon at the image-intensifier photocathode (i.e., for each discernible spot in images like those in B) are shown for the overall electron amplifications of 506×, 8,100×, and 129,600× (the y axis is normalized by the peak value in each histogram; the full x scale is increased by a factor of 16 from the left figure to the middle figure and from the middle figure to the right figure). The spots in the images (like those in B) were identified and the total number of electrons in each spot was evaluated using the functions of the ThunderSTORM plugin of ImageJ (Ovesný et al., 2014). For the spot detection with localization precisions at the pixel level (the peak pixel), we employed the “Wavelet filtering” (B-Spline order = 3 and B-Spline scale = 2.0) and the “Local maximum method” (Peak intensity threshold = 4.5 and Connectivity = 8-neighborhood). For the determination of the total number of electrons in a spot (and subpixel localization of each spot), we performed the Gaussian fitting of the image (i.e., the number of electrons/pixel in 11 × 11 pixels surrounding the peak pixel) and then integrated the best-fit function, using the Subpixel localization of molecules. These histograms were obtained using six 5,000-frame image sequences recorded at 10 kHz with a frame size of 13.4 × 13.4 µm on the focal plane, detecting 62,066, 459,156, and 510,165 photons (electrons emitted from the photocathode of the image intensifier) for overall amplifications of 506×, 8,100×, and 129,600×, respectively. They represent both the stochastic gain variations and the detectability of a photon image produced by the amplified electrons. See the histogram for 506×. The occurrences of the number of amplified electrons/detected photon sharply decreased when the number of amplified electrons was reduced below ≈650 electrons (the peak in the histogram). This is very likely due to a sharp reduction in the detectability of the spots produced by <650 electrons. Namely, when the signal intensity (the number of electrons) after amplification is small, the chance that the signal becomes less than the readout noise increases, because the readout noise pattern also fluctuates spatiotemporally (see C). (E) The probability of detecting a single photon was increased to 90.0% of the saturation level, at an overall electron amplification of 8,100×. Here, the number of detected photons per frame (mean ± SD); i.e., the number of discernible spots in the images like those in B (detected by the method described in D), is plotted as a function of the overall electron amplification (averaged over six 5,000-frame image sequences). With an increase in the overall electron amplification, the number of discernible spots increases. At an overall electron amplification of 8,100×, the number of discernible spots was 90.0% of the saturated number of spots (i.e., at the maximal overall electron amplification possible with the present instrument, which is 129,600× amplification). At the overall amplifications giving the saturated number of spots, virtually every photoelectron emitted from the photocathode is considered to be detected. Therefore, throughout the present research, we employed 8,100× as the overall electron amplification of the image intensifier (see “Ultrahigh-speed intensified CMOS camera system: Design and operation” in Materials and methods).