Explaining the Point-Spread Function (PSF), and how it can be used for deconvolution

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3D rendering of a sub-resolution fluorescent bead, imaged on a laser-scanning confocal microscope with the pinhole wide open (pseudo-widefield)

Suppose that you have a tiny fluorescent object, such as a 10nm-diameter fluorescent bead or even a single fluorescent molecule, and you try to observe it under a fluorescence microscope.  Provided that the object is bright enough, even though it is well below the resolution limit of your microscope you can still see the object; but it will appear larger than it really is.  Diffraction of light, which determines the microscope’s resolution limit, blurs out any point-like object to a certain minimal size and shape called the Point Spread Function (PSF).  The PSF, then, is the three-dimensional image of a point-like object under the microscope.  The PSF is usually taller than it is wide (like an American football standing on its tip), because optical microscopes have worse resolution in the depth direction than in the lateral direction.  Shorter wavelengths of light (such as blue light, 450nm) result in a smaller PSF, while longer wavelengths (such as red light, 650nm) result in a larger PSF and therefore worse resolution.  Also, the Numerical Aperture (NA) of the objective lens that you use affects the size and shape of the PSF:  a high-NA objective gives you a nice small PSF and therefore better resolution.  Surprisingly, the magnification of the objective lens does not affect the PSF – only the NA and wavelength matter.  You can use beads to measure Point Spread Functions for the objective lenses on your microscope to determine the resolution of each lens and also to see what condition each lens is in:  the PSF of a damaged objective lens is often large and possibly skewed in one direction or another.

Sometimes, a real specimen does indeed have single point-like fluorescent objects nicely separated from each other.  For example, cancer researchers studying the complicated process of DNA repair often irradiate cells and look to see what proteins localize on punctate sites of double strand breaks.  These nuclear foci are small enough that you are actually observing the microscope’s PSF when you image them.  In many cases, however, your specimen is a complicated arrangement of closely spaced fluorophores, and the PSF is not apparent in your images.  Nevertheless the PSF is hard at work, blurring out every fluorescent structure in your specimen as if tracing out the fine details with a fat paint brush.

Now, if we take the trouble to measure the PSF for a particular objective lens on our microscope, could we use what we know about the shape and size of the PSF to somehow undo its blurring influence in our specimen?  The answer is, “Yes!”.  Mathematically, the blurring of the PSF with the actual arrangement of fluorophores in the specimen is called a convolution of the specimen with the PSF:

convolution equation

It’s no accident that the symbol for convolution looks like a multiplication, since the two operators are related.  We don’t know what the actual Specimen looks like, but we record its Image in the microscope, and we can also record the PSF.  An operation called deconvolution reverses the effect of the PSF on the specimen, much like the division operator reverses the effect of a multiplication.  Practically speaking, we can never fully know what the specimen looks like, but by using iterative deconvolution algorithms we can remove some of the PSF’s blurring influence, particularly in the depth direction where the blur is worst.

Widefield (left) versus Deconvolved (right) images of a mouse kidney slice, imaged on a Zeiss AxioObserver with a 40x/0.85NA objective lens.

Widefield (left) versus Deconvolved (right) images of a mouse kidney slice, imaged on a Zeiss AxioObserver with a 40x/0.85NA objective lens.

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Is Cool the Rule for CCDs?

CCD picDigital cameras have been the primary means for recording fluorescence microscope observations for several decades. The three main types of digital cameras used in scientific microscopy applications are CCD, EMCCD, and sCMOS cameras. Each one of these types of camera has its own advantages. The sCMOS cameras are capable of blazing fast frame rates (hundreds of frames per second) to capture millisecond-scale dynamics. EMCCD cameras have high quantum efficiency, large pixels, and low noise, making them the camera of choice when very high sensitivity is required such as for detecting single fluorescent molecules. For nearly everything else, the interline CCD camera is likely your best choice: providing a good balance between sensitivity and resolution and between relatively low noise and moderate speeds, the CCD-equipped microscope is the workhorse of many research labs.

Research-grade CCD cameras range in price from $2,000 to $20,000, depending on acquisition speed, read-out noise, and depth of cooling. Most high-performance CCD cameras are cooled to a temperature between 0 and -30˚C. Cooling adds the significant cost of a thermoelectric device and also requires that the sensor be hermetically sealed to prevent damaging condensation on the sensor. But how does the costly addition of cooling actually affect the performance of the CCD camera? For rigorous life sciences research, which applications require a cooled CCD, and which ones do not?

The Cameras

We compared an uncooled Lumenera Infinity 3-1UR (list $4250) against a cooled Roper Scientific Coolsnap HQ2 (list $16,840). The most relevant specifications for the two cameras are shown in Table 1. Both cameras incorporate the Sony ICX285 sensor, so some parameters such as the resolution, pixel size, and quantum efficiency (QE) will be identical. Other parameters such as the bit depth and read noise will be governed by the electronics used to digitize the signal. The biggest difference is in the dark current, which is reduced from about 1e- to 0.001e- by cooling the HQ2’s sensor.

Specification Lumenera Infinity 3-1UR Roper Scientific Coolsnap HQ2
Image Sensor Sony ICX285 Sony ICX285
Resolution (pixels) 1392 x 1040 1392 x 1040
Pixel Size (um) 6.45 x 6.45 6.45 x 6.45
Quantum Efficiency (500nm) 62% 62%
Bit Depth 14 bits 14 bits
Full Well Capacity (e-) 18,500 16,000
Read Noise (e-) 6 5.5
Dark Current (e-/s) < 1 0.001
Sensor Temperature +37˚C -30˚C

Table 1: Comparison of camera specifications


Case Study #1: Fixed-cell microscopy

Figure 1: Alexa 488-labeled actin filaments in fixed endothelial cells imaged with A) cooled and B) uncooled cameras.

Figure 1: Alexa 488-labeled actin filaments in fixed endothelial cells imaged with A) cooled and B) uncooled cameras.


Fixed cells and tissues are labeled with relatively bright and stable fluorophores, making fluorescence microscopy on these samples a relatively routine endeavour. Figure 1 shows actin filaments in fixed endothelial cells labeled with Alexa Fluor 488 (FluoCells Prepared Slide #1, Life Technologies, F36924). The cells were imaged on a Zeiss AxioObserver inverted fluorescence microscope using an X-Cite 120 fluorescence lamp, a 40x/0.75NA Plan-Neofluar objective lens, and either the Infinity or Coolsnap camera (we consistently captured with the Coolsnap camera first). With the lamp set to 50% power, we used an exposure time of 1 second which filled most of the dynamic range of each camera without saturating.   Under these imaging conditions, there was no discernible difference whatsoever between the images taken by the two cameras. Both cameras produced sharp, clear images of the actin filaments with no difference in noise or background level. We also reduced the exposure time incrementally from 1s down to 100ms to mimic imaging of dimmer fluorophores, but the two cameras produced identical results in all cases.

Case Study #2: Live-cell microscopy

Figure 2: Paxillin-GFP expressing CHOK1 cells imaged with a 3s exposure time on A) cooled and B) uncooled cameras.

Figure 2: Paxillin-GFP expressing CHOK1 cells imaged with a 3s exposure time on A) cooled and B) uncooled cameras.

Living cells with fluorescent protein tags are more difficult to image: the fluorescence is typically weaker than with fixed-cell probes, the illumination power is often lowered to minimize photobleaching and phototoxicity, and shorter exposures may be required to capture cellular dynamics. Figure 2 shows CHOK1 cells expressing the focal adhesion protein Paxillin-GFP (cells courtesy of Claire Brown, McGill University, Montréal, Canada). The cells were imaged on a Zeiss AxioObserver microscope using a 63x/1.4NA objective with the lamp power reduced to 25% and a 3 second exposure time. Again, both cameras were able to capture superb images of the focal adhesions under these conditions: there was no difference in the image quality despite the fact that one camera was cooled and the other was not.

Figure 3: Paxillin-GFP expressing CHOK1 cells imaged with a 500ms exposure time on A) cooled and B) uncooled CCD cameras.

Figure 3: Paxillin-GFP expressing CHOK1 cells imaged with a 500ms exposure time on A) cooled and B) uncooled CCD cameras.

To achieve a faster frame-rate, we lowered the exposure time to 500ms and captured the low-light level images shown in Figure 3. Although obviously noisier, the two cameras are equally noisy and the focal adhesions are still readily trackable. The uncooled CCD camera achieves the same result as its considerably more expensive cooled counterpart for this challenging live-cell microscopy application.

Uncooled camera performance

Many microscopists assume that an uncooled CCD camera is not good enough for demanding live-cell imaging applications; but these experiments demonstrate that cooling the sensor is completely unnecessary. Why does the uncooled camera perform so well?

A good CCD camera for fluorescence microscopy should have a high Quantum Efficiency (a measure of the sensitivity of the sensor), high resolution (lots of pixels), high read-out speeds, and low noise. The first 3 parameters are completely independent of the camera temperature. Only the noise depends partly on temperature. CCD cameras have two main sources of noise:

  1. The read noise is the variation (or uncertainty) in reading out the values on the CCD sensor, primarily due to electronic components. Read noise varies with the read-out speed, but for these research-grade cameras it is generally limited to ± 6 electrons (e-) per pixel, independent of the exposure time. The maximum number of electrons that fit in each pixel of the image (called the full-well capacity) is more than 16,000 for the two cameras tested, so if you have enough light to fill at least half of the camera’s full-well capacity, the read noise is nearly negligible as in Figure 2. On the other hand, in Figure 3 where the signal is less than 10% of the full-well capacity, the read noise becomes apparent. Read noise, however, is still independent of the sensor temperature and is nearly identical for the two cameras tested.
  2. A dark current (or “dark charge”) accumulates in the sensor during longer exposures due to thermal processes, and the dark current noise is the statistical variation (or uncertainty) in the dark current level. The dark current noise does depend on the temperature of the sensor as well as the exposure time. You can measure and subtract the dark current background itself by closing the shutter and capturing a dark image, but the dark current noise has a randomness to it that can’t be subtracted. Cooling the camera can reduce the dark current level (and associated noise) to essentially zero for exposure times on the order of seconds. Even for the uncooled camera, however, the dark current noise of <1 is much lower than the read noise and therefore doesn’t contribute to the image.

In summary, cooling a CCD sensor only helps to lower the dark current and doesn’t significantly affect the other sensor parameters; but in the well-designed Infinity CCD, cooling wasn’t necessary to reduce the dark current well below the read noise of the camera, rendering the dark current noise negligibly low even for demanding live-cell fluorescence microscopy experiments.

Why do we still cool our CCD cameras?

Originally, CCD cameras had high dark current and it was necessary to cool them, particularly for astronomy applications that can require minute-long exposure times. But since about 1990, new technology for scientific-grade interline CCD sensors has lowered the dark current by about a factor of 1000 to well below the read noise of the camera. The low dark current makes cooling the sensor unnecessary even for rigorous fluorescence microscopy applications, provided exposure times are limited to no more than 10 seconds. It is likely that many users choose a cooled CCD camera even for routine fluorescence microscopy simply for historical reasons.

Cooling is still required in other disciplines, such as in vivo bioluminescence imaging or astronomy, where exposure times can be a full minute or longer.   For very low-light level applications, such as single-molecule detection or fast spinning-disk confocal microscopy, the dominant noise component is still the read noise and not the dark current noise: cooling the sensor will not improve the Signal to Noise Ratio for these photon-starved applications. Instead, for low-light level applications, the interline CCD should be set aside in favour of the added sensitivity of an Electron-Multiplier CCD (EMCCD) camera. EMCCD sensors have such a low read noise that the dark current noise becomes dominant: cooling the EMCCD sensor to about -80˚C is indeed required to lower the dark current noise.


Pawley, J. B. (2006). More Than You Ever Really Wanted to Know About CCDs. Handbook of Biological Confocal Microscopy. J. B. Pawley. New York, Springer: 918-931.

Spring, K. R. (2000). “Scientific Imaging with Digital Cameras.” BioTechniques 29(1): 70-76.

Joubert, J., Y. Sabharwal and D. Sharma (2011). “Digital Camera Technologies for Scientific Bio-Imaging.Part 3: Noise and Signal-to-Noise Ratios.” Microscopy and Analysis Sept 2011.

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Colour blindness and pseudo-colour

Did you know that about 10% of men are colour blind?  This means that if you are in a room giving a seminar to just 20 people with a split of roughly half men and half women, chances are there is at least one colour blind person in the room.

It is really frustrating for colour blind people when microscopy images are shown in red and green. They simply do not see the co-localization and are unable to judge the meaning and quality of the data.

Be sensitive to your colour-blind audience members, and consider changing your colour coding!  For multi-panel figures use grayscale for the individual images – your eyes are more sensitive to grayscale than to red and blue especially. Only use colour in the overlay. Use green and magenta or red and cyan instead of green and red. The overlay or co-localized regions will appear white.

colour blindness2

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Any way you slice it: a comparison of optical sectioning techniques

Confocal microscopy has become an essential tool for life sciences researchers.  The confocal’s ability to optically slice through thicker specimens, excluding the out-of-focus light while imaging just the focal plane, makes it the technique of choice for high-resolution fluorescence microscopy.  But with several different kinds of confocal microscope available, which one should you choose for your experiment?

Let’s look at three different kinds of confocal microscope, with a particular emphasis on how well they perform optical sectioning and the quality of the resulting images.  The laser-scanning confocal is the “original” confocal, and can still be considered the gold standard, particularly for fixed samples.  For live-cell imaging, a well-equipped spinning-disk confocal can give you fast frame rates and can be less phototoxic to the cells.  Finally, if budget is a concern for you, we consider whether the grid-based optical sectioning microscope (sometimes called “structured illumination”, not to be confused, though with the superresolution techniqute of the same name) will be adequate.

Optical sectioning performance (and microscope performance in general!) actually depends on the thickness of the specimen and the density of the labeling, so we will compare the confocals using 3 samples of different thicknesses:

  1. Thin (5um): Cultured BPAE cells (Molecular Probes Prepared Slide #1)
  2. Intermediate (15um):  Mouse kidney section (Molecular Probes Prepared Slide #3)
  3. Thick (35-50um): 3D Culture of mammary epithelial cells (courtesy of Hui Wang, OCI)

Laser-scanning confocal

The classic laser-scanning confocal scans a focused laser beam back and forth across a sample, in a raster pattern.  At each position, the focal point is imaged through a pinhole onto the detector – the pinhole blocks out-of-focus light from being detected.

A confocal isn’t really necessary for a sample as thin as the fixed BPAE cells:  when the widefield image stack is focused appropriately, the actin filaments are already sharp and well-contrasted from the background.  Nevertheless, this thin sample (essentially one 1um-slice-thick, except where it bulges around the nucleus) with its sharp features helps us to see the overall quality of a single slice.  As expected, the confocal excludes the out-of-focus light, so that as you move the focus away from the plane of the cells, the field rapidly becomes dark rather than blurry.

The thick sample nicely shows how the laser-scanning confocal can optically section a specimen into many slices, easily going as deep as 50um (and for many biological samples up to 100um or deeper, depending on the density of the labeling). The laser-scanning confocal performs optical sectioning without compromising resolution:  in fact, it gives you a small resolution improvement over widefield (although this is not terribly obvious, even in side-by-side images).  Its main drawback is acquisition speed:  to maximize the quality I used 1024 x 1024 pixels, sequential imaging of 3 channels, and averaged 4 images per slice, so for 25 slices through the kidney the image stack took about 6 minutes.

Spinning-disk confocal

A laser-scanning confocal is relatively slow, scanning a single focused spot across the sample and measuring the fluorescence intensity one pixel at a time.  The spinning disk sweeps about 1000 beams of light around the sample in parallel, and images them through a disk with a thousand pinholes onto a sensitive camera.  This is the spinning-disk confocal’s main advantage over it’s laser-scanning cousin:  speed!  However, to achieve decent speeds they are typically configured with a 512 x 512 pixel EMCCD camera, which sacrifices resolution to give you large, super sensitive pixels.

For the kidney tissue, the spinning disk does a decent job of optical sectioning but the lack of resolution is apparent…

Spinning-disk pixelation

… especially when you zoom in.

Optical sectioning suffers for the thicker specimen:  the thicker your sample, the more scattered light is generated which sneaks in through the wrong pinhole and reduces the confocality.  This is why spinning disks should be used for faster live-cell imaging and are not really the right tool for fixed slides.


I was pleasantly surprised to discover that the Apotome could, indeed, produce confocal-like optical sectioning for the not-too-thick kidney slice: there is no doubt that much of the blur has been removed, and when you move completely out of focus the image is black.

For the thicker sample, the Apotome image is very noisy (despite setting the algorithm to its maximum smoothing), and more-or-less unuseable except maybe near the surface.  The reason for this is that, as the sample gets thicker, the grid pattern that is projected into the image gets obscured by the out-of-focus blur.  I would say that grid-based optical sectioning is limited to samples that are at most 20um thick.


My thanks to Dan Stevens of Carl Zeiss Canada for help with acquiring the Apotome images; Hui Wang of OCI for providing the 3D culture of mammary epithelial cells; and of course my team Miria, Judy, and Feng at the AOMF.

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