Generic terms and rules for fluorescence microscopy

Detection efficiency. Those photons which are emitted by the specimen towards the aperture of the objective lens, and not absorbed in any of the optical components finally hit a pixel of the charge coupled device (CCD) sensor or photomultiplier (PMT) of a laser scanning confocal (or multy-photon) microscope. With a given probability - the quantum efficiency - each photon generate (or not) a photo electron. Therefore the efficiency of collecting the emitted fluorescence is determined by the numerical aperture (NA; the mean fluorescence intensity increases with NA⁴) see ¹ and the transmission of the objective lens, the transmission of the dichroic mirror and the emission filter and finally the quantum efficiency of the camera. The photo electrons are collected in the ‘well’ of the CCD pixel during exposure, and finally the accumulated charge is converted into gray value units by the analog-digital (AD) converter of the camera. Depending on the gain of the AD-converter one gray value unit typically corresponds to a few (1-4) photo electrons.

Signal to noise ratio. At low light level imaging the number of photons hitting each pixel of the sensor statistically varies and follows Poisson distribution. This is called the photon shot noise. The hallmark of the Poisson distribution is that the variance (s²) of the number of events (photons or photo electrons) in each pixel equals to their number. In addition, the digitized gray values are burdened by the variance added by the dark current and the read out noise of the camera. Considering gentle (low light level, short exposure time) imaging of otherwise bright fluorophores, the only significant source of noise is the photon shot noise. The relative error of the measurements as well as the perceived noise or the graininess of the image is inversely proportional to the signal to noise ratio (SNR=intensity/s) which is based on the standard deviation (s). Thus twice stronger illumination results double s², but only times s, so the signal to noise ratio improves by .

The tradeoff between photo-dynamic effects and the SNR. Photo-toxicity is an inherent side effect of fluorescence microscopy, therefore it is important to minimize the intensity and duration of fluorescence excitation. As a rule of thumb, better the SNR more the photo-toxicity is. SNR can be improved without increasing photo-toxicity by using a fluorophore with higher quantum yield, or optics and a CCD camera with better detection efficiency. However, usually these options are not available, therefore the smallest sufficient SNR has to be determined, and excitation intensities decreased accordingly. As another rule of thumb, during setting up image acquisition is that the illumination intensity has to be decreased until the image looks grainy, and then, a bit more or less intensity is used based on high or low SNR is desired. The sufficient photon count or gray value intensity can be calculated for a given SNR based on the photon shot noise characteristic and error propagation².

Dynamic range. At high light level the number of photo electrons (charge) that a pixel can collect is limited by the full well capacity of the camera. However, typically the AD-converter reaches its highest value before the number of photo electrons reaches the limit of the full well capacity, the maximal charge in electrons that one pixel can hold during exposure. The dynamic range of the sensor is given by the ratio of the full well capacity and the read out noise and is typically smaller than the range that the possible gray values span. E.g. a typical 12bit camera (possible gray values are 0-4095; like Cooke SensiCam QE, Photometrics Coolsnap series, Hamamatsu Orca ER) has full well capacity of ~15,000 e^- and read out noise ~8 e^- root mean square = 1:1875 dynamic range (this is an example, these values slightly vary with manufacturer / model). However, the dynamic range of the sensor is not a typical limitation in biological applications. It is important to set illumination intensity and exposure time not to saturate the sensor. Saturation leads to loss of information and inaccurate intensity measurements. Saturated areas can cause further image processing artifacts when using spatial filtering in Fourier domain. If high intensities are needed for low photon shot noise and superior SNR, switch the camera to ‘low gain’, ‘high multiplyer’ or ‘high light level’ mode, if such options are available.

Resolution in xy. CCD cameras specific to fluorescence microscopy have small resolution typically (0.26-1.3 megapixel). This is because the information content of a high magnification microscopic view field is curtailed by diffraction or Raleigh limit. E.g. using a high quality 60x NA=1.4 lens at l=535 nm of emission the smallest distance between two distinguishable fluorescent spots is 0.61l/NA=0.61*0.535mm/1.4 =233 nm. The above lens projects a 60 times bigger image ~14 mm on the sensor if no magnification changer (optovar) is used. The most widely used 1.3 megapixel CCD chips have 6.45 mm pixels, so the camera resolution is the double of the resolution of the microscope at this magnification. This double resolution is optimal to capture the complete information content provided by the optics of the microscope, according to the Nyquist Sampling Theorem. The mm/pixel calibration of acquired images is calculated by dividing the pixel size of the sensor by the magnification of the lens and the optovar.

While the diffraction limit renders close-by objects indistinguishable with conventional light microscopy, the diffraction limit does not reject information on the spatial localization (x,y position), or the size of fluorescent objects. I.e. sub-resolution dislocations or size changes of individual fluorescence objects can be detected. This is exploited in our organelle motion assay utilizing Optical Flow ³, or in the mitochondrial swelling assay using ‘Thinness Ratio’ or ‘Optimized Spatial Filtering Technique’².

When designing biological experiments the signal to noise ratio is often the greater concern over resolution. Decreasing the resolution by binning pixels in the camera results in dramatic improvement of the SNR. This is because photo electrons collected from a larger area will result to the gray value of each pixel. Moreover, acquisition of smaller images spares efforts during data storage and image processing. Certain image processing maneuvers discussed below require quadrangular images with a size equals power of two for fast computation. In our applications typically capturing 512x512 images proved to be optimal.

Resolution in z. The optical thickness of the imaged plane of a wide-field microscope with an NA=1.4 lens at l=535 nm emission is given by 2nl/NA² = 2*1.33*0.535mm/1.4² = 0.73 mm, where n is the refraction index of the medium. In cells thicker than this (which is usually the case) there will be out of focus mitochondria above and below this plane. To capture the whole cell in focus, z-stacks are used, with 0.8 mm spacing, or typically to decrease photo-dynamic effects, a more coarse 1-1.5 mm step size is suggested.

Image storage and playback. The AD converter of fluorescence microscopic monochrome CCD cameras digitizes at 12-16 bit, and images are stored in 16bit unsigned integer values. While the dynamic range of the detector is a lot smaller than the range provided by 16bits of integer values, during calculations with images the 16bit data storage is often insufficient. E.g., background subtraction as rounded integer numbers at very-low signal levels can introduce ‘bit noise’, such the rounding is reflected in the signal. Some calculations, like ratio calculation require small [0-1] fractional pixel values, while corrected FRET calculation requires multiplication of intensities, which can exceed the 16 bit range. DF/F₀ normalization and filtering in Fourier domain often requires the use of negative numbers as ‘pixel intensities’. Therefore Image Analyst converts all image data to 32bit floating point (real) values which has ~10 digits precision between 10^-38 and 10⁺³⁸, positive or negative.

During play back or printing images only a small part of the greater dynamic range of the recorded data can be visualized. This scaling of visualized images (including saving 8 bit RGB images) always have to be distinguished from the full 16 bit integer or 32bit floating point data storage. The visualized range of intensities is often given in percentile of the fluorescence intensity histogram. In this way each image of an image sequence can be individually scaled between the intensity values given by these percentages, providing good visibility of structures, when the overall intensity of the image changes frame to frame. In addition scaling for visualization can be nonlinear using gamma correction. Gamma correction means that the shown brightness of a pixel in the picture is proportional to the fluorescence value on the power of 1/g. Images of neurons expressing mitochondrial fluorophores typically very bright over the soma, and dim over the more distant neurites. An elevated gamma value (1.3-1.6) facilitates visualization of dim details, without excessive saturation of bright areas in the image.

Reference List

   1.   Yuste, R.; Lanni, F.; Konnerth, A. Imaging Neurons, Cold Spring Harbor Laboratory Press: 2000.

   2.   Gerencser, A. A.; Doczi, J.; Töröcsik, B.; Bossy-Wetzel, E.; Adam-Vizi, V. Biophys J 2008, 95(5), 2583-98.

   3.   Gerencser, A. A.; Nicholls, D. G. Biophys.J. 2008, 95, 3079-99.