Setting up the simulation frame
The aim is to simulate the images acquired by a camera when a Bessel beam is scanning through a Drosophila embryo. The first step is to simulate the image produced on the camera by a single fluorescent molecule excited by a Bessel beam. To this extent, consider the situation depicted in the following scheme:
The fluorescent molecules which are far away from the Bessel beam are not excited and won't contribute to the image formation (dark green stars). The fluorescent molecule hit by the Bessel beam is excited and emits fluorescence (light green). The molecule is not perfectly aligned to the axis of the Bessel beam (see magnified view in the circle), and it is also in a different plane with respect to the focal plane of the imaging optics (dashed line). This means that:
- The intensity of the fluorescence light emitted by the molecule will be proportional to the intensity of the Bessel beam, calculated at the position where the molecule is (for 2-ph excitation the fluorescence is proportional to the square of the Bessel beam intensity). The intensity of the Bessel beam can be calculated according to the N.A. of the illuminating objective, the ref. index of the medium, the wavelength of the illumination light, and the thickness of the focussed annulus of light (see Bessel Beam Simulation).
- The image of a point emitter (a fluorescent molecule, assumed much smaller than the microscope PSF) on the camera depends on the detection optics (N.A.), the emission wavelength, and the defocusing (i. e. the distance of the fluorescent molecule from the camera focal plane). This means that we only need to compute a 3D PSF which will be the same for all the molecule. Different molecules will have different values of the defocus and different intensities, which will add incoherently to form the final image on the camera.
The C code used to implement the simulation is here
The Embryo iself is simulated as a collection of N points, distributed randomly inside a 3D ellipsoid:
The Embryo is 500 µm long, 180 µm wide and 180 µm thick, with its major axis on the X axis. Each point represents a "fluorescent molecule".
The SPIM image formation is simulated by scanning the Bessel beam in the YZ plane (i. e. illuminating from the X axis). For each YZ position of the Bessel beam, the molecules that are excited (i. e. the ones which are not "too far away" from the Bessel beam axis) contribute to the camera image as mentioned above. As a result, we obtain a sequence of images, each representing the molecules excited by the Bessel beam at a certain YZ position.
SPIM image reconstruction
For each acquired camera image we compute either the sum of all the 41 pixel, or only the value of the central pixel.
- The refractive index of the space in which the fluorescent molecules are is water (n=1.333)
- The Bessel beam used to illuminate the molecules is calculated using an N.A. of 0.2, λ=920 nm, and a N.A. ratio of 0.95
- The voxel size of the illumination PSF used in the simulations is 0.5 µm.
- The image of a fluorescent molecule on the camera is calculated by using an N.A. of 0.2, λ=520 nm (GFP emission), and N.A. ratio of 0 (i. e. full aperture).
- The voxel size of the detection PSF used in the simulations is 0.5 µm.
- The camera field of view is 17.5 µm x 505 µm
- The beam is scanned in 370 steps of 0.5 µm either in the vertical (i. e. YZ) plane, or horizontal (XZ) plane
- The line profiles are acquired along the white lines
As evident from the line profiles, acquiring only the central pixel improves both the axial and the lateral resolution.