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The pixel values in a fluorescence image depend upon numbers of detected photons
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Blur & noise are inevitable
From photons to pixels
Chapter outline
The big picture of fluorescence imaging
Images in fluorescence microscopy are formed by detecting light – and such small amounts of light that it can be thought of in terms of individual photons. The photons are emitted from fluorescent molecules within the sample being imaged. Sometimes these photon-emitting molecules may be the very things we are interested in studying, but often they have only been introduced to the sample because they have the helpful property of fluorescing when in the presence of the (otherwise non-fluorescent) molecules or structures we would really like to see.
Either way, the most that the image can tell us is how much light was emitted from any particular point. From this information we make our interpretations, such as about the presence of absence of some feature, about the size and shape of a structure, or about the relative concentration of a molecule. But in no case are we seeing the feature, structure or molecule directly in the recorded images: we only have measurements of numbers of photons we could detect.
We will not give much attention here to what any particular number of photons emanating from a sample really indicates from a biological point of view – this would depend too much upon the design and details of the experiment, i.e. on the cells, stains and other substances involved. We can, however, often make general assumptions, such as that if we were to see (on average) twice as many photons originating from one region as from another, the number of fluorescing molecules must be around twice as high in the first region[1]. But before we can worry about such things, we first need to concentrate upon how accurately we can even determine the number and origins of photons being emitted from the sample, given the limited quality of the images we can actually record.
Recording images
A: The basic setup
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B: The specimen is illuminated; fluorophores become excited
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C: Light is emitted; some enters the objective lens and is detected
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Figure 1: A (very) simplified diagram showing the steps of image formation in fluorescence microscopy.
Once a specimen has been prepared and is waiting underneath the microscope, the basic process of recording a fluorescence image comprises four main steps (summarized in Figure 1):
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Fluorophore excitation. The fluorescent molecules (fluorophores) first need to be raised into an excited state. This happens upon the absorption of a photon, the energy (i.e. wavelength) of which should fall into a range specific to the fluorophore itself. This is carried out by illuminating the specimen, e.g. with a lamp or laser.
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Photon emission. When returning to its ground state, each fluorophore may emit a photon – this time with a lower energy (i.e. longer wavelength) than the photon previously absorbed.
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Photon detection. Most emitted photons can be thought of, rather informally, as 'shooting off in the wrong direction', in which case we have no hope of detecting them. But a proportion of the light should enter the objective lens of the microscope and be focussed towards a detector. When a photon strikes the detector, it is registered as a 'hit' by the release of an electron (when we are lucky; detectors are imperfect so this might not occur, meaning the photon is effectively lost).
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Quantification & storage. After fixed time intervals, the charges of the electrons produced by photons striking the detector are quantified, and from these quantifications pixel values are determined. A larger charge indicates more photons, which translates into a higher pixel value.
Errors and imprecisions
From the above summary, it is clear that we are quite some distance away from knowing exactly how much light is emitted from the specimen: most photons do not reach the detector, and many that do are still not registered. But since we can expect to always lose track of a similar proportion of emitted light – perhaps 90% – this does not matter much: we can expect all parts of the image to be similarly affected, so relative differences in brightness would still be reflected in our pixel values. However, there are two more critical ways in which the images we can record are less good than the images we would like:
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Uncertainty in space. Ideally, all light originating from a particular point in the specimen would strike the detector in exactly the same place, and therefore end up contributing to exactly the same pixel. In practice, however, the light beginning from one point cannot be focused back to a single point on the detector. Consequently, it can end up being spread over several pixels. The end result is that the image is blurred.
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Uncertainty in brightness. When an image is blurry we would also expect it to be smooth, but this is not usually what we get in fluorescence microscopy. Rather, there are seemingly random variations in brightness everywhere throughout the image: the noise. Some noise can come from imprecisions when determining the charge of small clouds of electrons quickly. But, more curiously, the emission of the photons is itself random, so that even if we detected every photon perfectly we would still get noisy images.
These issues are depicted in Figure 2.
A: Ideal imaging – a direct view of 'reality'
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B: More realistic imaging – a blurred and noisy view
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Figure 2: The difference between what we might wish to image, and what we actually can image. In both cases (A and B), the 'real' scene is shown on the left. Ideally, the small colored spots in reality would directly map to colored spots of a related size and separation in the image (A). However, the light emitted from these spots would actually end up producing larger objects in the image, which can then blur together (B, center). Noise is further added to this blurriness to give us the best image we can really record (B, right).
The twin issues of blur and noise do not affect all images equally. For example, blur can cause us to misjudge the size of something by several hundred nanometers, but if the thing we are measuring is much larger than this then the error may be trivial. Also, if we are detecting many thousands of photons then the uncertainty due to noise may be extremely small relative to the numbers involved. But very often we are interested in measuring tiny structures in images containing only tens of photons at their brightest points. In these cases, the effects of blur and noise cannot be ignored.
1. This assumes a linear relationship, which does not always hold (e.g. if there is dye saturation, or high laser powers are used for illumination).