Photon-free (s)CMOS camera characterization for artifact reduction in high- and super-resolution microscopy

Modern implementations of widefield fluorescence microscopy often rely on sCMOS cameras, but this camera architecture inherently features pixel-to-pixel variations. Such variations lead to image artifacts and render quantitative image interpretation difficult. Although a variety of algorithmic corrections exists, they require a thorough characterization of the camera, which typically is not easy to access or perform. Here, we developed a fully automated pipeline for camera characterization based solely on thermally generated signal, and implemented it in the popular open-source software Micro-Manager and ImageJ/Fiji. Besides supplying the conventional camera maps of noise, offset and gain, our pipeline also gives access to dark current and thermal noise as functions of the exposure time. This allowed us to avoid structural bias in single-molecule localization microscopy (SMLM), which without correction is substantial even for scientific-grade, cooled cameras. In addition, our approach enables high-quality 3D super-resolution as well as live-cell time-lapse microscopy with cheap, industry-grade cameras. As our approach for camera characterization does not require any user interventions or additional hardware implementations, numerous correction algorithms that rely on camera characterization become easily applicable.

grade cameras approach the specifications of scientific-grade cameras and are increasingly used in the scientific community [8][9][10][11][12][13][14][15] . Especially for those cameras, a precise characterization and correction of the large pixelwise variability is indispensable.
Here, we developed a fully automated camera characterization pipeline, which determines pixel-and exposure time-dependent noise, offset and gain maps that are the basis for numerous camera correction algorithms. Our pipeline does not require any specific camera illumination, as it relies solely on dark current and associated thermal noise. In addition to gain, offset and noise maps, it also allows for the explicit consideration of dark current and thermal noise in the image reconstruction, which is of particular importance for long exposure times in SMLM or low light level live-cell imaging. We demonstrate that we can accurately characterize diverse (s)CMOS cameras and use the calibrations to avoid bias in 2D and 3D SMLM and in diffraction-limited imaging. Our camera characterization algorithm is implemented for the popular software packages Micro-Manager 16 as well as ImageJ/Fiji 17 and enables (s)CMOS specific corrections for the broad imaging community.
Camera characteristics are conventionally determined by evaluating mean and variance of the signal in each pixel over many images at several light levels 1 . The mean and variance of the signal with no light reaching the camera correspond to offset and read noise squared, respectively. Due to the stochastic and discrete nature of photon detection, the gain can be calculated as the ratio of the variance and mean signal at different light levels. Thermal excitation is an alternative source for excited electrons, resulting in dark current that increases both the offset and thermal noise and, with it, the overall noise. Accordingly, a calibration loses its validity when a different exposure time is used for imaging. This holds particularly true for long exposure times or uncooled cameras.
We turn this source of error to our advantage and use thermal excitations to fully characterize the camera without any light reaching the detector. This is possible as thermally excited electrons follow Poisson statistics just as photoelectrons. Photon-free camera characterization is based solely on dark current and thermal noise (Figure 1a), using the linear relation between exposure time and dark current to generate different signal levels ( Figure 1b). Extrapolation to 0 ms exposure time gives the baseline (i.e. the offset free of thermal effects) as well as read noise (i.e. the noise free of thermal effects). Additionally, the explicit knowledge of the dark current and thermal noise as a function of exposure time now allows for computation of thermal effects at arbitrary exposure times (Figure 1c). For comparison, we used the traditional approach of varying light levels at a single frame exposure time of 10 ms (Figure 1d,e). Notably, the increased mean offset of 0.56 counts as compared to the photon free measurement equals the expected average dark current for 10 ms. For further verification, we calibrated an uncooled CMOS camera twice and found no considerable difference for all parameters (Supplementary Figure 1). We then compared the predictions of our approach to experimentally directly determined pixel-dependent offset and noise at different exposure times (Figure 1f). These comparisons showed high similarity, with average relative errors less than 0.4 % for the mean pixel values and 1.3 % for the noise. For the gain estimation (Figure 1e), we additionally compared our results with the single shot fluorescence method presented by Heintzmann et al. 18 that is based on out-of-band information from diffraction limited fluorescence images. The relative deviation in the median gain by the different methods was below 3.4 %. To additionally consider variations in sensitivity (e.g. due to differences in quantum efficiency) between neighboring pixels, we optionally added the flat-fielding approach of Lin et al. 5 and multiplied the flatfield map with the median gain to calculate the photon response map. However, for the cameras tested, the pixel-topixel variations in the flatfield map were very little (Supplementary Figure 2). Note that our approach does not correct for possible nonlinearities in the camera (Supplementary Figure 3), which would require more extensive characterization and correction routines 19 .
Precise knowledge of the relevant (s)CMOS characteristics encoded in the offset, noise and photon response maps is crucial for accurate fitting in single molecule localization microscopy 1,5 (SMLM). This holds especially true in the vicinity of hot pixels, which show increased offset and noise that strongly depend on the exposure time (Supplementary Figure 4). (s)CMOS-specific SMLM fitters 1,6 which are based on maximum likelihood estimation (MLE) 20 can achieve the theoretically achievable precision as given by the square root of the Cramer-Rao lower bound (CRLB). The camera maps generated by our approach (Figure 1) result in formally correct consideration of both dark current and thermal noise in (s)CMOS specific fitting (Supplementary Note 1) and we integrated the workflow into our SMLM software SMAP 21 .
To visualize the effect of (s)CMOS characteristics on SMLM, we simulated experiments of astigmatism-based 22 3D SMLM using measured maps of a latest generation, cooled scientific-grade CMOS camera (Fig 2a,b) and typical fluorophore parameters for traditional DNA point accumulation in nanoscale topography (DNA-PAINT) 23 (i.e. long exposure time and high photon numbers), (direct) stochastic optical reconstruction microscopy (STORM) 24 (i.e. short exposure time and medium photon numbers), and photoactivated localization microscopy (PALM) 25 (i.e. short exposure time and low photon numbers) (Methods). When (s)CMOS specific fitting was not applied, regions close to pixels of high dark current show a high bias in the 3D localization coordinates (Figure 2c,e), even for DNA-PAINT for which sCMOS specific SMLM fitting is often neglected 26 . Application of sCMOS specific fitting largely removes the bias (Figure 2d,f,g), and restores the theoretically achievable root mean square error (Figure 2h) for all SMLM modalities.
To validate our simulation results with experimental data, we performed 3D DNA-PAINT 23 using the same cooled scientific-grade CMOS camera. One might expect the bright fluorescence signal to be significantly higher than thermally generated signal. However, emitter dwell-times are in the 1 s regime, so dark current can play a pronounced role. Our experiments (Figure 2i,j) confirm the simulation results that the proximity of uncorrected high dark-current pixels leads to shifts in the localized coordinates. Although high dark-current pixels are relatively sparse on cooled, scientificgrade cameras, this bias locally misplaces structures in 3D (Figure 2k,l), easily exceeding nanometer localization precisions 26 . As expected from the simulations, the resulting distortion ( Figure 2 k-n, Supplementary Video 1) is highly spatially dependent and changes its direction over only a few hundred nanometers. Consequently, even cooled sCMOS cameras should be characterized carefully and corrected for thermal effects for unbiased SMLM reconstructions. Besides DNA-PAINT, such characteristics (i.e. long exposure times and high photon numbers) are also relevant for STORM under resolution-optimized conditions 27 . We next investigated if our approach can render uncooled, economic industry-grade CMOS cameras (Supplementary Figure 1) usable for high-quality 3D SMLM. Compared to sCMOS cameras, industry-grade CMOS cameras show higher dark current, higher noise and generally less uniform pixel properties 9 (Figure 3a,b, all characteristics shown in Figure 1d-f). In simulations, these lead to an even larger bias in the localizations. Especially for PALM, local bias exceeded 50 nm laterally and 150 nm axially (Figure 3c,e). Again, consideration of pixel-dependent effects removes the bias (Figure 3d,f,g) and restores the theoretically achievable root mean square error ( Figure 3h The potential of an uncooled, industry-grade CMOS camera becomes visible when we used it for 3D PALM 25 , i.e. SMLM with photoconvertible fluorescent proteins. PALM has lower signal levels as compared to STORM and DNA-PAINT, which is particularly challenging in presence of camera noise and for 3D SMLM. Following our photon-free camera characterization and applying the camera maps in CMOS-specific fitting, we could well resolve the 3D structure of clathrin coated pits by the same low-cost camera ( Figure 3 i-j). 3D STORM 24 (Figure 3k) on the nucleoporin Nup107 (ref. 28 ) clearly resolved individual corners of the nuclear pore complex (Figure 3l) in the lateral projection and parallel lines in the axial projection ( Figure 3m) stemming from the nucleo-and cytoplasmic rings. This indicates a resolution better than 57 nm in the axial direction 29 , achieved with this uncooled, but properly characterized industry-grade camera. Thus, we could show that with our approach, lowcost cameras exhibit only slightly reduced performance compared to sCMOS cameras, an important development in light of their recent popularity for SMLM [8][9][10]12,14,15 . Besides the conventional (s)CMOS corrections for pixel specific noise, gain and offset, our results indicate the benefit of characterizing and correcting for the effects of dark current and associated thermal noise in high-and super-resolution microscopy, both for uncooled and cooled cameras. To make our approach easily accessible for the imaging community, we implemented the automated camera characterization via electron noise tool (ACCeNT) in the popular open-source software Micro-Manager 16 and ImageJ/Fiji 17 (Supplementary Note 2). All relevant camera properties, including thermal effects, can be determined without user intervention and there is no need for additional hardware implementations. Thus, existing algorithms that demand proper camera characterizations, like the ones we used in this work, become applicable by a broad audience.   uncooled CMOS camera. Dark current and thermal noise squared are proportional to the exposure time, so the temporal dependence can be determined from the slope of linear fits. The y-intersects of the fits reveal the baseline as well as the read noise squared, free from thermal effects. Since thermally generated signal follows Poisson statistics, the variance is proportional to the mean, with the proportionality factor corresponding to the pixel gain. c, Baseline, dark current, read noise, thermal noise and gain maps are calculated pixel-wise as in b. Optionally, we acquire a single bright image for flat-field correction. From these maps, we calculate the exposure-time dependent offset, variance and photon response maps. These maps can then be used as input for existing camera correction algorithms for images recorded at arbitrary exposure times. d, Histograms of pixel values obtained by photon-free characterization (blue curve) and traditional characterization of using varying light levels (black dashed curve). The traditional characterization overestimates baseline and read noise by the thermal effects for the corresponding exposure time. e, Distribution of the gain determined via different approaches (pixelwise histogram for the photon-free and varying light levels approaches, histogram of outcomes from multiple determinations of the mean gain from the 1-shot approach). Symbols above the curves indicate the medians (diamond for photon-free approach, square for vary light levels approach, circle for 1-shot fluorescence). f, Comparison of pixel offset and noise distributions at different single frame exposure times either predicted using the calculations shown in c, or directly determined from pixel-wise means and standard deviations.

Figure 2: Camera calibration for thermal effects circumvents systematic fitting errors in SMLM
Maps of dark current (a) and noise (b) at 500 ms single frame exposure time for a scientific-grade CMOS (sCMOS) camera cooled to the manufacturer's calibration setpoint of -10 °C. Simulations of 3D DNA-PAINT via astigmatism-based PSF shaping using this camera reveal a particular pattern in the localization bias close to pixels of high dark current, both laterally (c) and axially (e) when not applying (s)CMOS-specific fitting that corrects for pixel-wise effects including thermal effects. Explicit application of (s)CMOS specific fitting largely removes the bias for DNA-PAINT (d,f) as well as STORM and PALM (g) and restores the theoretically achievable root mean square error in the localizations (h). i, Experimental 3D DNA-PAINT data of the nucleoporin Nup96 in U2OS cells using the same cooled sCMOS camera. The image is rendered as an overlay of the pixel dark current map (red) and the SMLM reconstruction with no camera correction (magenta) and with CMOS correction (green). j, Zoom into boxed region in i. k,l, The structure of a nuclear pore complex (indicated by the boxes in m,n) becomes shifted in the vicinity of a pixel of high dark current, both in axial (k) and lateral (l) direction when neglecting individual pixel characteristics including thermal effects in the fitting pipeline. m, Axial view of the region indicated in j, also shown in Supplementary Video 1. n, Lateral close up of the nuclear pore complex indicated in m. As expected from the simulation, the shift features a high spatial dependence (m,n), which even changes its sign (indicated by the red arrows in n).

Camera calibration
For the photon-free calibration, all light to the camera chip was blocked by screwing a lid to the camera mount. Before starting the measurement, the camera was pre-run to give the detector time to thermally equilibrate either to the targeted cooling temperature (-10 °C as this was the manufacturer's calibration setpoint) or warming up to the operating temperature in case of uncooled cameras. We acquired around 8,000 to 20,000 sets of typically 5 to 10 different exposure times. To maintain a constant average detector temperature, recording was performed in a nested manner, i.e. we changed the exposure time after each camera frame and then repeated acquisition of all exposure times.
Initially, we used custom-written scripts in Micro-Manager, Fiji and MATLAB for data acquisition and analysis, but later implemented the entire workflow into independent Micro-Manager and Fiji ACCeNT plugins (see next paragraph). After recording of raw data as described in the former paragraph, Fiji was used to process the TIFF stacks. For each exposure time and pixel, the mean value and standard deviation were calculated and saved as TIFF files: One after another, the stack corresponding to one exposure time was imported to Fiji and the "z-project" function was called with projection type "Average Intensity" for the mean value or projection type "Standard Deviation" for the standard deviation. The resulting TIFF files were imported into MATLAB for further processing. For each pixel linear functions were fitted using the polyfit function to (i) the mean value as a function of the exposure time to determine the baseline from the y-intersect and the dark current per time from the slope, (ii) the variance (i.e. the standard deviation squared) as a function of the exposure time to determine the read noise squared from the y-intersect and the thermal noise squared per time from the slope, and (iii) the variance as a function of the mean value to determine the gain (i.e. the conversion factor from electrons to ADU counts) from the slope. For each pixel, the exposure time dependent offset was calculated as the baseline plus the dark current per time multiplied by the single frame exposure time. For each pixel, the exposure time dependent noise squared was calculated as the read noise squared plus the thermal noise squared per time multiplied by the single frame exposure time. For each pixel, the photon response was calculated as the median of the gain map for all pixels multiplied by the pixel-wise value of the flatfield map. To find the flatfield map, we exposed the camera to a homogeneous illumination via ambient light and applied the algorithm presented by Lin et al. 5 .
We implemented the photon-free calibration workflow including the automated nested data acquisition, fitting of individual pixel properties and calculation of exposure time dependent camera maps as the ACCeNT plugin for Micro-Manager 2. Additionally, we implemented the fitting of individual pixel properties and calculation of exposure time dependent camera maps as an ACCeNT plugin for Fiji. The latter is intended to be used for processing of data acquired with software different from Micro-Manager 2, e.g. if the microscope is run using Micro-Manager 1.4 or the manufacturer's software. For Micro-Manager 1.4 users, we provide a script for the automated nested data acquisition. We checked the consistency of all implementations against each other.

Microscope
All data was acquired on a custom-built microscope as described in the following. ). An additional short pass filter (FESH750, Thorlabs) was used before the camera to block light from a focus lock laser. The focus lock laser (785 nm, Toptica) was coupled into the excitation beam path using an additional dichroic mirror, reflected off the coverslip-buffer interface of the sample, and its position was detected using a four-quadrant photodiode. The photodiode output was used to maintain the z-position of the objective lens constant with respect to the sample for active z-drift compensation.
The microscope hardware and data acquisition was handled via Micro-Manager 1.4.22 using custom-written software 31 . When imaging using an industry-grade CMOS camera, the excitation laser was run constantly. When imaging using the cooled, scientific-grade sCMOS camera, the excitation laser was triggered on during the common exposure of all lines of the camera. In all cases, the UV laser for active photoswitching in PALM and STORM experiments was triggered at the camera frame rate, but the pulse length was dynamically adjusted to aim for a constant number of active emitters per frame.

U2OS cells NUP107-SNAP for STORM
U2OS Nup107-SNAP samples stained with Alexa Fluor 647 for STORM imaging were prepared as previously described 29 .

U2OS cells immunostained for DNA-PAINT
U2OS cell immunostained for microtubules for DNA-PAINT imaging were prepared as previously described 6 using anti beta-tubulin antibody (T5293; Sigma-Aldrich).

U2OS cells Nup96-eGFP for DNA-PAINT
Cells were seeded as previously described on high-precision 24 mm round glass coverslips 33 . In short, coverslips (No. 1.5H, catalog no. 117640, Marienfeld) were cleaned in a methanol:hydrochloric acid (50:50) mixture overnight before washing them repeatedly with ddH2O and drying them in a laminar flow hood. Before usage, clean coverslips were additionally irradiated with UV for 30 min.
U2OS Nup96-mEGFP cells were seeded onto the coverslips in such a density, that they reach a confluency of 50 to 70% on the day of fixation (typically 2 days after seeding

Fluorescent bead samples
100 nm sized TetrackSpeck beads (Thermo Fisher) were diluted 1:40 in 100 mM MgCl2 in H2O and incubated for 3 min on coverslips. Before imaging and PSF calibration via z-stacks, the bead solution was replaced by H2O.

Data acquisition
PALM imaging was performed using an uncooled, industry-grade CMOS camera (µeye UI-3060CP-M-GL R, IDS). Fixed U2OS cells were imaged in buffer containing 95 % D2O and 50 mM Tris/HCl pH9. Raw data was acquired in HILO illumination at 561 nm and laser output powers of 20 mW to 50 mW. The single frame exposure time was set to 50 ms.
DNA-PAINT imaging of tubulin in U2OS cells was performed using an uncooled, industry-grade CMOS camera (µeye UI-3060CP-M-GL R, IDS). Fixed U2OS cells were imaged in buffer containing 500 mM NaCl, 1x PBS, 40 mM Tris/HCl pH8 and imager strands (I1 650, i.e. Atto655, Ultivue) at a concentration of about 500 pM. Raw data was aquired in HILO illumination at 640 nm and a laser output power of 70 mW. The single frame exposure time was set to 500 ms.
DNA-PAINT imaging of Nup96 in U2OS cells was performed using a cooled, scientific-grade CMOS (sCMOS) camera (Edge 4.2bi, PCO). Fixed U2OS cells were imaged in buffer containing 500 mM NaCl, 40 mM Tris/HCl pH8 and imager strands (I1 650, i.e. Atto 655, Ultivue) at a concentration of about 500 pM. Raw data was acquired in HILO illumination at 642 nm and a laser output power of 4.5 mW. The single frame exposure time was set to 500 ms.
Diffraction limited TIRF imaging of AP-2 in U373 cells was performed using an uncooled, industrygrade CMOS camera (µeye UI-3060CP-M-GL R, IDS). Live U373 cells were imaged at room temperature in growth medium. Raw data was acquired in shallow TIRF illumination at 488 nm and a laser output power of 0.1 mW. The single frame exposure time was set to 1000 ms.

Image data analysis
SMLM data was fitted and analyzed as previously described 28 using our custom-written, open-source superresolution microscopy analysis platform SMAP 21 in MATLAB (Mathworks). The software is available at github.com/jries/SMAP. In case of (s)CMOS specific fitting, the predetermined camera maps were applied for the exposure time of the respective experiment.
3D SMLM data (STORM, PALM, DNA-PAINT) was fitted with an experimentally derived PSF model measured via z-stacks of 100 nm sized fluorescent beads as previously described 6 . For STORM data, the localizations were filtered for a lateral localization precision better than 12.7 nm, a relative log-likelihood value better than -2.9, and the first 600 frames were filtered out. For PALM data, the localizations were not further filtered. For DNA-PAINT data, the localizations were filtered for a localization precision from 0 to 12 nm and a z-coordinate of -200 nm to 100 nm. 2D DNA-PAINT data was fitted with a Gaussian PSF model and the localizations were filtered for a localization precision better than 30 nm and a PSF width of 100 to 175 nm. Diffraction-limited TIRF images were processed using the NCS software and ACsN software, respectively, as provided by the authors. As input, we use the camera maps determined via the photon-free approach described in this work, encoding the pixel-wise properties for gain, offset, and noise in case of NCS and gain and offset in case of ACsN. We parameterized the NCS MATLAB "single pixel with normalization"-algorithm by an alpha weight factor of 10, a pixel size of 0.0977 µm, an emission wavelength of 0.525 µm, a numerical aperture of 1.49, and 25 iterations. We parameterized the ACsN MATLAB app with a numerical aperture of 1.49, an emission wavelength of 525 nm and a pixel size of 108 nm, turned the video filter off and the parallel CPU option on.

SMLM simulation
Raw 3D SMLM data were simulated in MATLAB using an experimentally derived PSF model for the microscope described above, experimentally derived camera characteristics via the photon-free approach described in this work, and photon counts parameterized by DNA-PAINT, STORM and PALM experiments described above. Camera data was simulated using a projected camera pixel width of 98 nm and the emitters were placed on the center of each camera pixel. Each emitter position was simulated for 1,000 times with the distribution of photon counts drawn from the experimentally derived distribution of the photon counts per emitter and per frame. Poisson noise was added to the photon distribution over the experimental PSF and the fluorescence signal was converted to ADU counts. The camera baseline was added, the dark current was added corresponding to the respective single frame exposure time (50 ms for PALM and STORM, 500 ms for DNA-PAINT), read noise and thermal noise was added corresponding to the respective single frame exposure time. The synthetic raw 3D SMLM data was then fitted either using a (s)CMOSspecific fitter with explicit consideration of pixel-to-pixel variations of the camera properties including dark current and thermal noise, or neglecting pixel-to-pixel variations and using the average values of the camera properties instead. The bias for each emitter position was determined as the deviation of the mean fitted coordinate from the ground truth.
For the expected root mean square error (RMSE), we followed the same approach as described above, but did not draw the photon counts from a distribution. Instead, we simulated all emitters with the same photon counts using the mean photon counts from the distribution (i.e. 3,420 photons for PALM, 9,000 photons for STORM, 35,100 photons for DNA-PAINT in case of the scientific-grade CMOS camera, and 1,900 photons for PALM, 5,000 photons for STORM, 19,500 photons for DNA-PAINT in case of the industry-grade CMOS camera). The theoretically achievable precision was calculated via the square root of the Cramér-Rao lower bound (CRLB) 20 according to the particular PSF shape 6 .

Data availability
Example data can be downloaded from https://rieslab.de/#accent.

Code availability
The software for the data acquisition and analysis used in this paper is available at https://github.com/ries-lab/Accent/releases and https://github.com/jries/SMAP.

Supplementary Figures
Supplementary Figure 1: Repeated photon-free characterization of the same camera shows reproducibility of the approach Comparison of repeated photon-free characterizations of the same camera show high similarity (blue and orange curves). For comparison: Histograms of pixel values obtained by photon-free characterization (blue curve and orange curve) and traditional characterization of using varying light levels (black dashed curve). Distribution of the gain determined via different approaches (pixelwise histogram for the photon-free and varying light levels approaches, histogram of outcomes from multiple determinations of the mean gain from the 1-shot approach). Symbols above the curves indicate the medians (blue diamond and orange circle for photon-free approach, square for vary light levels approach, circle for 1-shot fluorescence). and plot the mean signal per illumination condition as a function of the mean signal of the local 10x10 pixel neighborhood for selected pixels. a shows 0 % to 72 % of the dynamic range of the camera, b shows a zoom into 0 % to 3 % of the dynamic range and c shows a zoom into 0 % to 0.06 %. While the light response of the camera is mostly linear over a large part of the dynamic range, the zoom in (c) reveals nonlinearities for some pixels particularly for about the first 200 (photo)electrons above the offset. For the DNA-PAINT experiments presented in this work, the mean background per pixel was 301 photons (and the fluorescence signal above the background was much higher), so we operate the camera in the linear regime. d shows the mean signal for a part of the camera. e,f, We recorded dark images at different exposure times and plot the mean signal of all pixels as a function of the exposure time. e shows the plot for 0 ms to 4,000 ms and f shows a zoom into 0 ms to 200 ms. The plot reveals three different regimes of dark current for the camera: The dark current appears proportional to the exposure time for 0 ms to 30 ms (corresponding to high to medium framerates often used in STORM and PALM imaging), some transitioning behavior for exposure times from 40 ms to 200 ms, and again appears proportional to the exposure time for 200 ms to 3000 ms. For the experiments presented here, we characterized the camera via the photon-free approach for exposure times from 350 ms to 3000 ms and operate the camera at 500 ms for the DNA-PAINT imaging, so the characterization as well as the experiments are performed in a linear regime.  Figure 4: Uncorrected CMOS pixel-to-pixel variations affect localization accuracy both laterally and axially a, A fluorescent bead was positioned such that its diffraction limited image was captured close to two pixels of increased noise. b shows a zoom into the region indicated in a including the pixel noise characteristics and the repeated localizations via astigmatism-based 3D PSF fitting. Magenta dots show the localizations when not using an (s)CMOS-specific fitter that takes care of individual pixel characteristics and green dots show the localizations when using an (s)CMOS-specific fitter that explicitly considers individual pixel characteristics including noise. Gaussian fits to line profiles of the localization distribution inside the boxed region indicated in b show that the localization precision (i.e. the standard deviation of the localizations) is increased when not using the (s)CMOS-specific fitter both laterally (c) and axially (d). e,f, Repeating the same experiment, but capturing the image of a bead in proximity to a pixel of high offset resulting from high dark current. In this case, the mean localized position is significantly shifted both laterally (g) and axially (h). The axial shift occurs because the axial position is being estimated from the shape of the PSF which becomes apparently distorted by the pixel of increased brightness when not applying a (s)CMOS-specific fitter that explicitly considers individual pixel characteristics including offset.