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By virtue of the linearity property of optical non-coherent imaging systems, i.e., . Image(Object 1 + Object 2) = Image(Object 1) + Image(Object 2). the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as a weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the ...
The ability of a lens to resolve detail is usually determined by the quality of the lens, but is ultimately limited by diffraction.Light coming from a point source in the object diffracts through the lens aperture such that it forms a diffraction pattern in the image, which has a central spot and surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern, and ...
In both cases the numerical aperture of the objective is 1.49 and the refractive index of the medium 1.52. The wavelength of the emitted light is assumed to be 600 nm and, in case of the confocal microscope, that of the excitation light 500 nm with circular polarization. A section is cut to visualize the internal intensity distribution.
Diffraction geometry, showing aperture (or diffracting object) plane and image plane, with coordinate system. If the aperture is in x ′ y ′ plane, with the origin in the aperture and is illuminated by a monochromatic wave, of wavelength λ, wavenumber k with complex amplitude A(x ′,y ′), and the diffracted wave is observed in the unprimed x,y-plane along the positive -axis, where l,m ...
The effect of the contrast transfer function can be seen in the alternating light and dark rings (Thon rings), which show the relation between contrast and spatial frequency. The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample.
As a pencil of light goes through a flat plane of glass, its half-angle changes to θ 2. Due to Snell's law, the numerical aperture remains the same: NA = n 1 sin θ 1 = n 2 sin θ 2. In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or ...
Memorial in Jena, Germany to Ernst Karl Abbe, who approximated the diffraction limit of a microscope as = , where d is the resolvable feature size, λ is the wavelength of light, n is the index of refraction of the medium being imaged in, and θ (depicted as α in the inscription) is the half-angle subtended by the optical objective lens (representing the numerical aperture).
To calculate back to φ e (x,u) the wave in the image plane is back propagated numerically to the sample. If all properties of the microscope are well known, it is possible to recover the real exit wave with very high accuracy. First however, both phase and amplitude of the electron wave in the image plane must be measured.