4.1. Quantitative fluorescence microscope comparison
Before using the presented method for quantitative microscope comparison, the fluorescence detectors and the fluorescent test layer must fulfil certain requirements. The fluorescence detectors must be used in their linear regimes and the test layer must satisfy the following assumptions. The initial fluorescence intensity (the intensity before bleaching has occurred) of the test layer should be proportional to the excitation intensity, the fluorophore number density and the exposure time. Also, bleaching of the test layer should be mono-exponential, with the rate of photobleaching proportional to the excitation intensity and independent of the fluorophore number density.
In a previous article (Ghauharali et al., 1998) it was demonstrated that for the confocal microscope, both the fluorescence detector and the initial fluorescence intensity of the test layer fulfilled the imposed requirements. The same tests were applied to the conventional microscope and it was found that also with this microscope, the detector and the initial fluorescence intensity of the test layer satisfied the assumptions made in the theoretical analysis of the method. For brevity, the results of these experiments will not be shown here.
To test whether the bleaching characteristics of the test layer fulfilled the requirements in both microscopes, we measured the bleaching behaviour of the test layer from an image series acquired in an arbitrarily chosen part of the layer. In Fig. 2 the mean fluorescence intensity and the standard deviation in a small region of interest (ROI; dimensions and position in the image chosen arbitrarily) within successive images in the series are plotted against the total single pixel exposure time as calculated with Eq. (6). Analysis of the bleach curves showed that in both microscopes the fluorescence intensity decay was bi-exponential instead of mono-exponential. As argued in detail earlier (Ghauharali et al., 1998), a practically mono-exponentially bleaching regime can be established through pre-bleaching of the test layer. By pre-bleaching, the contribution of the rapidly decaying exponential is deliberately significantly decreased, so that the remaining fluorescence intensity decrease is effectively determined only by the slowly decaying exponential. The rate of the slowly decaying exponential will be referred to as ‘the bleachrate’ in the following.
Figure 2. .50 s. In both figures the dashed curves represent fits with a mono-exponential function (correlation coefficients 0.94 (confocal) and 0.98 (conventional) and the solid curves are fits with a bi-exponential function (correlation coefficients > 0.99 for both microscopes). The insets show mono-exponential fits of the data after prebleaching.
Download figure to PowerPoint
Earlier (Ghauharali et al., 1998), it was demonstrated that in the confocal microscope the bleachrate was independent of the fluorophore concentration of the test layer and proportional to the excitation intensity, as imposed in the theoretical analysis of the method. Similar results were obtained for the conventional microscope. For brevity, these results will not be shown in this article.
Now that it has been established that with the selected microscopes and the fluorescent test layer the requirements for the validity of the theoretical analysis of the method are satisfied, the proportional excitation intensity and detection efficiency distributions of the microscopes can be determined and the microscopes can be quantitatively compared.
Determination of the proportional excitation intensity and detection efficiency distributions is done using Eqs (2) and (3). As indicated, the distributions can be determined from images of the fluorescent test layer, acquired before and after partial bleaching of the layer.
A typical image pair of the test layer acquired in the confocal microscope is shown in Figs 3(a) and (b). In both images a stripe- and spot-like pattern is visible. That these patterns are not caused by features of the test layer, but by spatial non-uniformities of the optical system of the microscope, can be seen from Figs 3(c) and (d). In these figures the proportional excitation intensity and detection efficiency distributions, C(rij) and D¯(rij), as derived from the images of the test layer shown in Figs 3(a) and (b), are displayed. It can be seen that these distributions are not uniform. In both the excitation intensity and the detection efficiency distribution, a stripe-like pattern is visible. This pattern is caused by the dichroic mirror of the microscope (see also Ghauharali et al., 1998). In the detection efficiency distribution, a spot-like pattern can also be seen. This pattern is caused by contaminations in the detection pathway of the microscope and is responsible for the dark spots in the images of the test layer.
Figure 3. ) from image pairs of the test layer, before and after bleaching, acquired from different and randomly chosen parts of the test layer (see also section 2). One of these image pairs is shown in (a) and (b). The same grey scale was used to visualize the images in (a) and (b).
Download figure to PowerPoint
A typical image pair of the fluorescent test layer acquired in the conventional microscope is shown in Figs 4(a) and (b). The accompanying proportional excitation intensity and detection efficiency distributions calculated from these images are shown in Figs 4(c) and (d). From these figures it can be seen that in this microscope also, the images before and after bleaching are not uniform and that the pattern is caused by spatial non-uniformities of the optical system of the microscope. The excitation intensity distribution is relatively uniform, but a ring-shaped region can be seen in which the excitation intensity is slightly (approximately 3%) higher. The detection efficiency distribution contains large dark regions, caused by contaminations of the optical elements in the detection pathway. Note that the magnification, M, in this microscope is a factor of two larger than in the confocal microscope (Fig. 3a).
Figure 4. . (a) Typical image of the fluorescent test layer before bleaching acquired in the conventional microscope. (b) Image of the region shown in (a) after bleaching. (c) Proportional excitation intensity distribution C(rij). (d) Proportional detection efficiency distribution D¯(rij). The same grey scale was used for the images (a) and (b). The distributions shown in (c) and (d) were determined as explained in the caption to Fig. 3.
Download figure to PowerPoint
For a quantitative comparison of the microscopes, the means and standard deviations of the proportional excitation intensity and detection efficiency distributions were determined and summarized in Table 1. From this table it is clear that for the present illumination and detection conditions, in the confocal microscope the excitation intensity is approximately a factor of 10 higher and the detection efficiency (which not only contains the extent of the detection volume (or the magnification) and the fluorescence collection efficiency of the microscope, but also CCD camera-related factors such as the quantum efficiency and the gain) approximately a factor of five lower than in the conventional microscope. It follows from the coefficients of variation (the ratio of the standard deviation and the mean; CV) in this table that over the entire image region variations of approximately 10% and 20% occur in the proportional excitation intensity and detection efficiency distributions in the confocal microscope, whereas in the conventional microscope these variations are approximately 5% in both distributions. This means that the excitation intensity and detection efficiency distributions of the conventional microscope are much more uniform than those of the confocal microscope.
Table 1. . Quantitative comparison of confocal and conventional microscopes.
Besides quantitatively comparing different microscopes, the method presented can also be used to assess the (long-term) stability of one microscope. The analysis described in the previous paragraphs was repeated after 2 and 4 weeks for the confocal and the conventional microscopes, respectively. Comparison of the results of the second analysis (also shown in Table 1) with those of the first shows that no large changes have occurred, indicating that, in the time intervals investigated, both microscopes were stable.
4.2. Image standardization and shading correction
In the previous section we have shown that the experimentally determined proportional excitation intensity and detection efficiency distributions can be used to quantitatively compare two different microscopes. Here it will be demonstrated that the same distributions are used for specimen image standardization by way of shading correction. Before standardizing specimen images, the shading correction procedure will be illustrated and the concept of ‘standardized fluorescence units’ will be introduced.
It should be clear that if shading correction is applied to images of the fluorescent test layer itself, any structure in the image caused by non-uniformities of the microscopes must disappear. That this is the case is demonstrated in Fig. 5, which shows images of the fluorescent test layer acquired with the confocal and conventional microscopes. Figures 5(a) and (c) show the test layer images, respectively, in the confocal and the conventional microscopes before standardization. Figures 5(b) and (d) show the same images after standardization using the experimentally determined excitation intensity and detection efficiency distributions shown in Figs 3 and 4 and Eq. (5). It can be seen that the images after standardization are much more uniform than before, indicating that the procedure has indeed largely removed the image intensity variations caused by spatial non-uniformities of the optical pathways of the microscopes.
To make this visual inspection more quantitative, we calculated the means and standard deviations of the images before and after standardization and summarized the results in Table 2. Before standardization, image intensities are expressed in analogue-to-digital conversion units or counts. After standardization, so-called standardized fluorescence units (SFU) are used; these express the fluorescence of a specimen relative to that of the test layer used to implement the standardization. An SFU of 1.0 means that, under equal excitation and detection conditions, the fluorescence of the specimen is equal to that of the test layer. From Eq. (5) and the definition of the SFU it follows that when the test layer itself is used as a specimen, the intensities in the standardized image must be equal to 1.0. The results in Table 2 indicate that, whereas before standardization there is a large difference between the test layer image intensities, after standardization the difference has been eliminated and the standardized fluorescence is close to 1.0. Also clear from the table is that the CVs after standardization are much smaller than before standardization: over the entire image region, the procedure achieved an approximately fivefold and more than fivefold decrease of the image intensity variations for the confocal and the conventional microscopes, respectively.
Table 2. . Effect of image standardization on test layer image intensity variations in the confocal and conventional microscopes.aa The images before standardization were acquired in three different regions of the test layer. The images of region 1 are shown in Fig. 3 for the confocal and Fig. 4 for the conventional microscope.b Expressed in CCD counts.c Expressed in SFUs.
The results in Table 2 indicate that in spite of the large difference between the excitation intensity and the detection efficiency in both microscopes (see Table 1), the standardization procedure has effectively compensated the test layer images for differences related to both the magnitude and the distribution of the excitation intensity and the detection efficiency (including differences in the CCD cameras used for fluorescence detection) in both microscopes. Note that, as is inherent in the approach, differences due to the magnification (see Figs 3(a) and 4(a)), effectively causing differences between the volumes from which the generated fluorescence is projected onto a single pixel, have also been compensated (see also below).
A specimen consisting of 200 nm uniform fluorescent microspheres was used to further demonstrate the image standardization procedure. The specimen was imaged in both the confocal and the conventional microscopes and the images were standardized as described above. From the images before and after standardization the total single microsphere fluorescence was calculated.
Before standardization the total microsphere fluorescence was determined by summing the pixel values in ROIs within the primary microsphere images, sufficiently large to contain the entire microsphere and applying a background correction. In order to compensate for ‘trivial’ differences between the microscopes caused by different image exposure times, we divided the total microsphere fluorescence by the image exposure time. The obtained quantity, referred to below as the ‘total microsphere fluorescence rate’ (TMFR) is dependent only on the excitation intensity and the detection efficiency of the particular microscope.
After standardization the total microsphere standardized fluorescence (TMSF) was determined by summing the pixel values in ROIs within the standardized microsphere images. As discussed in section 2.2, the TMSF is dependent on the magnification of the microscopes and the number of pixels per microsphere must be equalized before the TMSF can be calculated. In our case the magnification in the confocal microscope was a factor of two smaller than in the conventional microscope. We compensated the confocal images by doubling the number of pixels, interpolating the intensities of the inserted pixels and then calculating the TMSF. For other magnification differences other pixel-insertion schemes must be used.
In Fig. 6, histograms of the total fluorescence of single microspheres before and after standardization are shown. Before standardization the ratio of the total microsphere fluorescence in the confocal and conventional microscopes can have any value, whereas after standardization this ratio should be close to 1.0 for the standardization procedure to be effective.
Figure 6. . Histograms of the total microsphere fluorescence rate (TMFR) and the total microsphere standardized fluorescence (TMSF). For each microsphere, the total fluorescence was calculated by summing the pixel values within a ROI sufficiently large to contain the entire sphere in the images before and after standardization. The effect of differences in the magnification M on these histograms is discussed in detail in the main text. A total of 40 microspheres were used to compile each of the histograms shown. (a) and (b) Histograms before and after standardization for the confocal microscope. (c) and (d) Histograms before and after standardization for the conventional microscope.
Download figure to PowerPoint
Inspection of the histograms before standardization shows that in the confocal microscope the fluorescence intensity is much higher and less uniform than in the conventional microscope. The difference in uniformity is consistent with the much smaller variations of the excitation intensity and detection efficiency distributions of the conventional microscope when compared with the confocal microscope (see Table 1). Comparison of the histograms after standardization shows that the difference between the microsphere fluorescence intensity in the confocal and the conventional microscopes has disappeared and that the difference in uniformity has been reduced significantly.
In Table 3, the means, standard deviations and CVs of the histograms in Fig. 6 are summarized. The results in this table confirm that before standardization there is a large difference between the microsphere fluorescence in both microscopes and that after standardization the total microsphere fluorescence is, as should be for an efficient standardization procedure, similar in both microscopes.
Table 3. . Total microsphere fluorescence before and after standardization in the confocal and conventional microscopes. a Expressed in CCD counts per unit time.b Expressed in SFUs.
After standardization the mean and standard deviation of the TMSF in the confocal microscope are somewhat higher than in the conventional microscope. This may be related to non-optimal shading correction, due to deviations from mono-exponential bleaching of the particular fluorescent test layer employed to implement the correction (see section 4.1). Note also that in the standardization of the images of the test layer a higher CV after standardization in the confocal microscope when compared with the conventional microscope can be seen (see Table 2).
From the results in Table 3 it follows that the CV of the TMSF of the confocal microscope is smaller after standardization, whereas that of the conventional microscope has not been reduced. As the standardization procedure only compensates for image intensity variations which are caused by the optical properties of the microscope, this indicates that, for this particular specimen, in the confocal microscope the image intensity variations are determined by both the optical characteristics of the microscope and the specimen, whereas in the conventional microscope the variations are dominated by the specimen. This is consistent with the higher degree of uniformity of both the excitation intensity and detection efficiency distributions of the conventional microscope when compared with the confocal microscope. The intrinsic CV of the microspheres is, according to the manufacturer of the spheres, approximately 10%. Considering that the standardization was not optimal, that a relatively small number of microspheres was used to calculate the histograms and the fact that under the present experimental conditions the CVs after standardization in the confocal microscope are larger than those of the conventional microscope (see Table 2), the experimentally determined CVs of 10% for the conventional and 20% for the confocal microscope are close to what can be expected.