Noise causes variance
in the intensity values above and below the “real” intensity value of the signal plus the background. The extent of deviation differs from one pixel to the next in a single digital image, with the maximum variance in an image referred to as the noise level (). Noise causes imprecision in measurements of pixel intensity values, and therefore a level of uncertainty in the accuracy of the measurements. To detect the presence of a signal, the signal must be significantly higher than the noise level of the digital image (). If the signal is at or below the noise level, the variation in intensity caused by noise will make the signal indistinguishable from the noise in quantitative measurements (). As the signal increases relative to the noise level, measurements of the signal become increasingly more precise (). The precision of quantitative microscopy measurements is therefore limited by the signal-to-noise ratio (SNR) of the digital image. SNR affects spatial measurements as well as intensity measurements; precise determination of the location of a fluorescently labeled object depends on SNR () (Churchman et al., 2005
; Yildiz and Selvin, 2005
; Huang et al., 2008
; Manley et al., 2008
One type of noise found in fluorescence microscopy digital images comes from the signal we are trying to measure. Measurements of stochastic quantum events, such as numbers of photons, are fundamentally limited by Poisson statistics (Pawley, 1994
). This means that the number of photons counted in repeated measurements of an ideal, unchanging specimen will have a Poisson distribution. The number of photons counted in a single measurement therefore has an intrinsic statistical uncertainty called Poisson noise (also referred to as shot noise, signal noise, or photon noise). The maximum variance in the number of counted photons that can be attributed to Poisson noise is determined by the Poisson distribution and is equivalent to the square root of the total number of detected photons. This formula applies to the number of detected photons, not
the arbitrary intensity values reported by detectors. Detected photons, p
, can be calculated from intensity values using the equation
is the full well capacity of the detector, imax
is the maximum intensity value the detector can produce, i
is the intensity value being converted to photons, and o
is the detector offset. The detector values can be obtained from the technical specification sheets available on the detector manufacturer's website.
Poisson noise cannot be reduced or eliminated. However, as the number of counted signal photons increases, the Poisson noise becomes a smaller percentage of the signal and the SNR increases. Working to increase the number of signal photons collected will therefore increase the accuracy and precision of quantitative measurements.
Fluorophores vary greatly in their intrinsic brightness and the rate at which they photobleach; an easy way to maximize signal is to choose a brighter and more photo-stable fluorophore (Diaspro et al., 2006
; Tsien et al., 2006
). The brightness of a fluorophore is determined primarily by its extinction coefficient and quantum yield, properties that are dependent on the fluorophore's environment (Diaspro et al., 2006
). It should be noted that new fluorescent proteins are routinely introduced that outperform their predecessors; it is therefore advisable to search the current scientific literature for the latest variants.
Fixed specimens should be mounted in a glycerol-based mounting medium (Egner and Hell, 2006
; Goodwin, 2007
) that contains an anti-photobleaching inhibitor (Diaspro et al., 2006
). No one anti-photobleaching reagent is the best, as each reagent is more or less effective for a given fluorophore (Diaspro et al., 2006
). Review the fluorophore manufacturer's product information or the relevant scientific literature (Shaner et al., 2005
; Giepmans et al., 2006
; Johnson, 2006
) to make the best choice of fluorophore and anti-photobleaching reagent for your specimen and experiment. Goodwin (2007)
provides a complete discussion of the importance of mounting medium choice to both signal intensity and resolution.
To get the brightest signal while minimizing specimen damage, it is important to use illumination wavelengths that will optimally excite the fluorophore and to collect as many of the emission photons as possible (Ploem, 1999
; Rietdorf and Stelzer, 2006
). Fluorescence spectra that show the absorption and emission efficiency of fluorophores are available from the manufacturer or in the scientific literature (for example, see Shaner et al., 2005
), and filter manufacturers provide spectra online that show the percent transmission of their filters across wavelength. It is important to compare the spectra for the fluorophore you are imaging to spectra for the fluorescence filter sets (and/or laser illumination line) to ensure you are using the correct wavelengths of light to excite the fluorophore and collecting as much of the emission light as possible (Ploem, 1999
; Rietdorf and Stelzer, 2006
). There are several useful online tools available for matching fluorophores to filters (for example, as of the date of this publication Invitrogen has a very useful tool on their website: http://www.invitrogen.com/site/us/en/home/support/Research-Tools/Fluorescence-SpectraViewer.html
In an epifluorescence microscope, the objective lens both illuminates the specimen and collects photons emitted from fluorophores to form the optical image. The numerical aperture (NA) of the objective lens (marked on the barrel of the lens after the magnification; Keller, 2006
) is an important determinant of the brightness of the optical image. The number of photons an objective can collect from a specimen (and therefore the brightness of the image) increases with NA2
. Brightness of an objective is also determined by properties such as transmission and correction for aberration (Keller, 2006
). Spherical aberration caused by the objective lens (Hell and Stelzer, 1995
; Goodwin, 2007
) or introduced by the specimen (Egner and Hell, 2006
) decreases image intensity (North, 2006
; Waters, 2007
; Waters and Swedlow, 2007
). Spherical aberration occurs when there is a relatively large difference in refractive index between the specimen and the lens immersion medium; for example, when an oil immersion lens is used to image a specimen in an aqueous solution such as cell culture medium (Egner and Hell, 2006
). Spherical aberration caused by refractive index mismatch generally increases with distance from the coverslip (Joglekar et al., 2008
). Spherical aberration can be addressed using water immersion objective lenses (Keller, 2006
), by using an objective lens with a correction collar (Keller, 2006
; Waters, 2007
), or by immersion oil refractive index matching (Goodwin, 2007
). For fixed specimens, spherical aberration is reduced by mounting fixed specimens in a mounting medium with a refractive index similar to that of the immersion medium (e.g., mounting medium with a high concentration of glycerol will have a refractive index close to that of standard immersion oil).
The number of photons reaching the detector that are collected and contribute to the intensity values in a digital image depends on the quantum efficiency (QE) of the detector, and how long the signal is allowed to integrate on the detector (usually referred to as the exposure time). QE is a measure of the percentage of photons reaching the detector that are counted (Moomaw, 2007
). The QE of research-grade CCD cameras most often used for quantitation of fluorescence images ranges from 60% to over 90%, whereas the QE of PMTs used in point-scanning confocals is much lower, usually 10–20% (although the effective QE is significantly less; see Pawley, 2006b
). QE values are available online from the detector manufacturer.
Increasing the exposure time allows the flux of photons coming from the specimen to accumulate (as electrons) in the detector, increasing the intensity values in the image—up to a point (Moomaw, 2007
; Spring, 2007
; Waters, 2007
). Detectors have a limited capacity to hold electrons; if this capacity is reached, the corresponding pixel will be “saturated” and any photons reaching the detector after saturation will not be counted. The linearity of the detector is therefore lost, and saturated images cannot be used for quantitation of fluorescence intensity values. Choosing to “crop out” saturated areas is not acceptable (unless they can be shown to be irrelevant to the experimental hypothesis) because it will select for the weaker intensity parts of the specimen. Saturation should be avoided by using image acquisition software to monitor intensity values when setting up the acquisition parameters ().
In most live biological specimens, saturation is much less of a problem than collecting enough signal to get adequate SNR images for quantitation. Many research-grade cooled cameras allow binning of adjacent pixels on the CCD chip. With all other acquisition parameters being equal, binning on the CCD chip increases the intensity of the pixels without increasing readout noise, resulting in a higher SNR digital image (Moomaw, 2007
; Spring, 2007
; Waters, 2007
). However, because the resulting pixels represent a larger area of the specimen (i.e., 4x larger with a 2 × 2 bin), binning decreases the resolution of the digital image (). In many low-light imaging experiments, however, the decrease in resolution is well worth the increase in SNR ().
Figure 3. Resolution and sampling. (A–C) Images of the same pair of 150-nm green fluorescent beads collected with a microscope (model TE2000U; Nikon), a Plan-Apochromat 100x 1.4 NA oil objective lens, and MetaMorph software. A camera with 6.45-µm (more ...)
Background fluorescence reduces dynamic range and decreases SNR.
Although it's true that background fluorescence can and must be subtracted from quantitative measurements of intensity, it is also very important to first reduce background as much as possible (, ). Background in an image effectively reduces both the dynamic range and the SNR. Dynamic range of a CCD camera is defined as the full well capacity of the photodiodes (i.e., the number of photons that can be detected per pixel before saturation) divided by the detector noise (Moomaw, 2007
; Spring, 2007
). High dynamic range is particularly important for collecting an adequate number of signal photons from both dim and bright areas of the specimen. Photons from background sources fill the detector, limiting the number of signal photons that can be collected before the detector saturates () and effectively decreasing dynamic range. In addition, recall that the number of photons counted defines the Poisson noise level in an image. Poisson noise is equal to the square root of the signal photons plus
background photons; higher background therefore means higher Poisson noise. Subtracting a constant background value from intensity measurements does not change the variance due to Poisson noise; the presence of background therefore reduces image SNR.
A common source of background in biological specimens is out-of-focus fluorescence. In fluorescence microscopy, the illuminating light is focused at the image focal plane by the objective lens, such that maximum excitation of fluorophores occurs at the focal plane (Hiraoka et al., 1990
). However, illuminating light above and below the image focal plane excites fluorophores above and below the image focal plane. Light emitted from these out-of-focus fluorophores is collected by the objective lens, and appears as out-of-focus background in the in-focus image of the specimen. In wide-field epifluorescence microscopy, adjusting the diameter of the field diaphragm to match the visible field of view minimizes the illumination of out-of-focus fluorophores (Hiraoka et al., 1990
) and reduces background (Waters, 2007
There are several microscopy techniques that serve to reduce the amount of out-of-focus fluorescence in the image. Confocal microscopes illuminate the specimen with a focused light source, while one or more corresponding pinholes at the image plane block out-of-focus fluorescence from reaching the detector (Pawley, 2006b
). Spot-scanning confocals scan the specimen point-by-point with a single focused laser beam, whereas multi-point or slit-scanning confocals (including spinning disk confocals) use multiple pinholes or slits to illuminate the specimen more quickly (Adams et al., 2003
; Tommre and Pawley, 2006
). Multi-photon microscopes illuminate the specimen with a focused high-power long wavelength laser, which results in excitation of the fluorophores through absorption of multiple photons at the same time only at the focal plane (Rocheleau and Piston, 2003
). In total internal reflection (TIRF) microscopy, fluorophores are excited with the evanescent wave of energy that forms when total internal reflection occurs at the boundary between media of different refractive indexes, usually the coverslip and the specimen (Axelrod et al., 1983
). Deconvolution algorithms can also be used to reduce the out-of-focus fluorescence in digital images post-acquisition (Wallace et al., 2001
Because out-of-focus fluorescence is a source of background, and background reduces SNR and dynamic range, shouldn't we always use one of the imaging methods that reduces out-of-focus fluorescence? The answer is not that simple. Each of the methods used to remove out-of-focus fluorescence has limitations, and may contribute additional noise to the image (Murray et al., 2007
). In specimens with low levels of out-of-focus fluorescence (which is often the case in adherent cultured cells), standard wide-field fluorescence microscopy may result in the highest SNR image (Murray et al., 2007
). Therefore, none of the different modes of microscopy is “better” than the other, only more or less appropriate for a particular specimen or application (Swedlow et al., 2002
; Murray et al., 2007
). When possible, empirical comparison of available modes is the most reliable way to ensure you are using the best imaging system for your application.
Any background that remains in a fluorescence microscopy digital image must
be subtracted from intensity value measurements to reveal the signal (). Consider two specimens, one with an average intensity value of 2,000 and the second with an average intensity value of 2,500. Without considering background, one might conclude that the fluorescence signal in these two specimens differs by 25%. However, if the background in each image measures 1,900, the difference is actually sixfold! Background should be subtracted following the equation
is the fluorescence intensity measured at each pixel i
(pixels in the object) or j
(pixels in the background), obj
is the object of interest, bkg
is the background, and N
is the number of pixels in the object of interest or the background. This equation corrects for different-sized regions of interest used to measure the object of interest and the background by calculating the background per pixel. This can also be achieved by using image analysis software to calculate the mean intensity value in a region of interest, as long as the number of pixels in the region of interest and the range of intensity values in those pixels are sufficient to give a precise mean (Cumming et al., 2007
). To avoid errors due to an inhomogeneous background, it is best to make background measurements using pixels that are immediately adjacent to or surrounding the object of interest (for examples, see Hoffman et al., 2001
or Murray et al., 2007
). This is especially important when making measurements of intracellular structures because the background in the cytoplasm is often different than the background outside of cells, and is usually inhomogeneous.
Fluorescence microscopy digital images are degraded by Poisson noise and by noise from the detector (Pawley, 1994
; Moomaw, 2007
; Spring, 2007
). Thermal noise is caused by the stochastic generation of thermal electrons within the detector, and is largely eliminated by cooling (hence the use of cooled CCD cameras; ). Read noise is generated by the amplifier circuitry used to measure the voltage at each pixel, and is usually the dominant source of noise in standard cooled CCD cameras designed for quantitative imaging. Read noise is usually expressed in the manufacturer's technical specifications as a number of electrons, meaning that the measured voltage will have a variance equal to that number of electrons (i.e., the lower the value, the lower the noise). Detectors that use signal amplification (e.g., PMTs and electron multiplying [EM] CCDs) introduce additional noise during the amplification process. For example, EM-CCD cameras amplify signal differences sufficiently to reveal clock-induced charging—stochastic variations in the transfer of charge from one pixel to another during read operations (Robbins and Hadwen, 2003
; Moomaw, 2007
). When possible, collecting more photons from the specimen to increase the signal (see ) will result in a higher SNR image than amplifying a smaller number of collected photons. The various sources of noise add as the sum of the squares:
The resulting total noise in the digital image defines a minimum expected variance in the measured intensity values. Differences in measurements that lie within the expected variance due to noise cannot be attributed to the specimen. Pawley (1994)
provides a thorough review of the different sources of noise in digital microscopy images.
Noise is not a constant, so it cannot be subtracted from a digital image. However, if multiple images of the same field of view are collected and averaged together (“frame averaging”), the noise will average out and the resulting mean intensity values will be closer to the “real” intensity values of the signal plus the background (Cardullo and Hinchcliffe, 2007
). Frame averaging is very useful when imaging fixed specimens with a higher noise instrument like a point-scanning confocal, but is usually impractical for quantitative imaging of live fluorescent specimens that are dynamic and susceptible to phototoxicity and photobleaching. For quantitative fluorescence imaging, noise added to the digital image during acquisition should be reduced as much as possible through choice of detector and acquisition settings ().