February 21, 2019
by Abhijit Marar
We decided to go back to our calculations to understand how the distance between the sample and the objective was affecting the radius of the hologram, the reconstruction distance and the transverse magnification. In SIDH (Self-interference digital holography), the light from a point source which is typically spread across 250 nm (~9 pixels) in an optimally configured wide-field fluorescence system is spread across 400-500 pixels while conserving energy. Due to this it is important to make sure that the signal is rising above the background noise. Earlier blog posts have discussed our efforts in trying to decrease the noise in the system. In the last month we decided to try to control the size of the hologram which has proven to bear more results than our earlier strategy.
Fig (a) above shows the radius of the hologram at the camera plane as a function of defocus when the camera is placed at a distance that is twice the focal length of the curved mirror in the interferometer( f = 300mm). It can be seen that as we move closer to the sample, the size of the hologram gets enormous, thus making it very difficult to capture the hologram on the camera because of low signal to noise ratios. On the other side of focus, the hologram shrinks to a point after 6 µm thus making it difficult for the camera to resolve the fringes in the hologram which is a necessity to reconstruct the images. This has been one of the major causes of our lower axial range (~4 µm) so far. Fig (b) shows that by moving the camera closer to the interferometer, the size of the hologram varies a lot less as one moves through focus and the radius is maintained within an acceptable range as determined experimentally. Moving the camera closer to the interferometer also helps break the ambiguity in the reconstruction distance one encounters while imaging using SIDH as shown below.
It can be seen that in Fig (2a), it is impossible to tell whether the sample is below or above focus due to the reflection across the axis of symmetry (x = 0). This ambiguity can be broken across the axial range of interest by placing the camera closer to the interferometer as can be seen in Fig (2b). Thus the combination of results shown in the Fig (b) and (2b) makes it very favorable to place the camera closer to the interferometer. It is important to note that by making this change one violates the "condition for perfect overlap" which has a detrimental effect on the two-point resolution of the system, however this will not affect us significantly (might make it slightly challenging to look at crowded emitters, but this problem can be solved by placing additional lenses in the system and relaying the back focal plane to control the total system magnification) since our goal is to localize the single-emitters eventually.
In the previous blog post we showed that we were able to look at holograms of 100 nm fluorescent beads (580/605) but we did not reconstruct them. We decided to image 100 nm fluorescent beads by making the changes suggested by our calculations.
The animation above shows the axial view of a 100nm fluorescent bead imaged at different focal planes (4 µm step size) across a 20 µm axial range. The variable magnification in the system is also reduced because of the new position of the camera. We have yet to find a solution to the spherical aberration that can be seen at the edges of the range. We have tried to image 40 nm fluorescent beads but we have at this stage only been able to look at the holograms without reconstructing them.
1) Try to image smaller emitters.
2) Calculate how precisely we can localize the reconstructed data in three dimensions.