Defocus distance

In real curvature sensors, a vibrating membrane mirror is placed at the telescope focus, followed by a collimating lens, and a lens array. At the extremes of the membrane throw, the lens array is conjugate to the required planes. The defocus distance can be chosen by adjusting the vibration amplitude. The advantage of the collimated beam is that the beam size does not depend on the defocus distance. Optical fibers are attached to the individual lenses of the lens array, and each fiber leads to an avalanche photodiode (APD). These detectors are employed because they have zero readout noise. This wavefront sensor is practically insensitive to errors in the wavefront amplitude (by virtue of normahzing the intensity difference). 

Cs is the spherical aberration coefficient. This phase shift by spherical aberration can be significant for short wavelength waves such as electrons. Fortunately, this phase shift can be offset by phase shift caused by defocusing the image. We can defocus the image and make the focal point at the distance further from the focal plane (i.e. weaken the lens power). The phase shift from defocusing the image is a function of the defocus distance (D) from the focal plane. 

The acoustic lens is able to translate axially along the z direction by variation of the distance between the specimen and the lens for subsurface visualization. That is, when the surface of the specimen is visualized, the acoustic lens is focused on the specimen (we denote z = 0 pm), and when a subsurface of the specimen is visualized, the acoustic lens is mechanically defocused toward the specimen (we denote z = -x pm, where x is the defocused distance). 

A direct removal of image Fourier coefficients from a reconstructed electron exit wave seems a most suitable way for resolution verification. Here, Figure 2 shows for the first time the contribution of Si (444) image Fourier coefficients to the separation of the 0.78A dumbbell distance in Si [112] in the phase of an electron exit wave. The focal series was recorded at Lichte defocus with the 0AM and reconstructed in 2001. 

Figure 1. Ray optical description of lens aberrations, (a) Perfect lens imaging a point P in the object plane onto a sharp point in the image plane, (b) Lens affected by spherical aberration, (c) Lens underfocused by a distance Z. (d) Lens overfocused by a distance Z. Spherical aberration and defocusing cause a blurring of the point P in the image plane.

The limits zmjn and zmax are the values of defocus at which the reflected rays just fill the area of the transducer thus for zmin < z < zmax all the reflected rays that enter the lens fall on the transducer, while for values of defocus outside that range some of the rays miss it altogether. The value z0 is the defocus at which the geometrically reflected rays are focused on the transducer at this point, as indeed at z = 0, ray optics breaks down because it does not allow for diffraction, although it does correctly predict the position of a minimum in V(z) at z0. The approximate expressions are valid when D/n > q, as is usually the case in a high-resolution acoustic microscope. In the approximation for z0, the quantity Ft is the ratio of the separation between the transducer and the back focal plane of the lens D — q/n) to the Fresnel distance for the transducer (na /Ao),... 

Fig. 14.2. Principle of filamentation. The beam first self-focuses and collapses due to the Kerr effect. Ionization at the non-linear focus then defocuses the beam. A dynamical balance establishes between both processes over distances much over the Rayleigh length...

Further publications have presented microscopic methods for the 3D determination of the velocity distribution in microchaimels by means of the 3D point spread function (PSF). With defocus, the spot diameter of a nanoparticle first increases, and then for larger displacements from the focus complex ring intensity patterns are developed. The full 3D pattern represents the PSF of the optical system and is determined mainly by the objective lens of the microscope system. The intensity pattern, i.e. the number and diameter of rings and the relative intensity of rings, gives information about the distance of the object from the imaging focal plane. Speidel... 

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