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Transfer functions and cameras
Published in Neil Collings, Fourier Optics in Image Processing, 2018
The transfer function approach is valid for an ideal isoplanatic optical system. This ideal system is one where the translation of an object point in the object plane produces a proportional translation of the image point in the image plane. The diffraction-limited OTF is the transfer function for an ideal imaging system which is free from aberrations. The shape of the diffraction-limited OTF as a function of frequency is determined by the limiting aperture of the system, for example, the circular frame of the lens. This has been calculated for both square and circular limiting apertures [90]. It decreases monotonically from a maximum at zero spatial frequency to zero at a cut-off frequency, which is equal to the reciprocal of the product of the f-number of the lens and the wavelength of the light. The f-number is the focal length of the lens divided by the lens aperture. Higher f-number lenses have lower cut-off frequencies.
Registration for Super-Resolution: Theory, Algorithms, and Applications in Image and Mobile Video Enhancement
Published in Peyman Milanfar, Super-Resolution Imaging, 2017
Patrick Vandewalle, Luciano Sbaiz, Martin Vetterli
In a real camera several non idealities contribute to a significant deviation from the pinhole model. The linear distortion introduced by the optics is represented by the point spread function (PSF). This is the impulse response of the imaging system, i.e. the image obtained when a point light source of infinitesimal size is placed in front of the system. Even when the system is perfectly focused, the image is not a point of infinitesimal size, but rather a disk of nonnegligible diameter. This measure describes the quality of the optical system. For example, lenses that are not ideal or are not precisely placed, result in an increase of the size of the point spread function. However, even in the ideal case, the point spread function has a non-negligible size. For an ideal lens with circular aperture, the point spread function is also called the Airy disk [8]. Its size is determined by the diffraction of the system, which is proportional to the wavelength of the light source and the aperture value (or f -number). Note that higher f -numbers correspond to a smaller aperture area, or less incident light. A large f -number corresponds to a large Airy disk and a strong low-pass effect (and at the same time a large depth of field). Conversely, a small f -number corresponds to a smaller Airy disk and sharper images.
Optics in Digital Still Cameras
Published in Junichi Nakamura, Image Sensors and Signal Processing for Digital Still Cameras, 2017
In reality, because this depends on the cross-sectional area of the light beams, the brightness of the lens (the image plane brightness) is inversely proportional to the square of this F-number. This means that the larger the F-number is, the less light passes through the lens and the darker it becomes as a result. The preceding equation also shows that the theoretical minimum (brightest) value for F is 0.5. In fact, the brightest photographic lens on the market has an F-number of around 1.0. This is due to issues around the correction of various aberrations, which are discussed later. The brightest lenses used in compact DSCs have an F-number of around 2.0. When the value of θ′ is very small, it can be approximated using the following equation in which the diameter of the incident light beams is taken as D. This equation is used in many books.
Application of extension rings in thermography for electronic circuits imaging
Published in Quantitative InfraRed Thermography Journal, 2022
A Cedip Titanium 560 M cooled thermographic camera with an InSb Focal Plane Array (FPA), a 640 × 512 pixel resolution and 15 µm pixel pitch was used for tests. The camera was equipped with a standard 50 mm (focal length), F/2 (f-number) lens. That choice was made for two reasons: lens mount using a standard metric thread M80, allowing for easy extension ring manufacturing and mounting, and camera software giving full access to its configuration, including user temperature calibration and non-uniformity correction (NUC) procedures. The camera was distributed by the manufacturer with a single 1/2” = 12.7 mm long, black anodised aluminium extension ring. Three additional black anodized aluminum extension rings were manufactured, two 30 mm long and one 60 mm long. For clarity, the 10 possible camera ring configurations were numbered from R0 (no ring) to R9 (132.7 mm long ring composed of the complete set of the four rings). The rings are shown in Figure 2 and the measurement setup is presented in Figure 3.
The Nyquist criterion and its relevance in phase-stepping digital shearography: a quantitative study
Published in Journal of Modern Optics, 2022
Awatef Rashid Al Jabri, Kazi Monowar Abedin, S. M. Mujibur Rahman
Before performing the actual shearographic experiments, we measured the speckle size on the captured image on the image sensor and compared it with the expected theoretical value. We covered one of the mirrors in the Michelson system (mirror 2), so that the light from mirror 1 enters the camera. We captured an image for each value of the F-number (focal length/aperture diameter of the imaging lens) selected by the camera software. We expanded each captured image by Photoshop, identified the individual speckles one by one on the expanded image. Each pixel must be visible as small squares in the expanded image (known as pixelation). We identified 10 speckles in different locations of the image and measured their diameters (in pixels), and calculated their average. Since the pixel size on the image sensor is known (3.9 μm), we could estimate the average speckle size (in microns) for each value of the F-number selected. On the other hand, the theoretical speckle size is given by the following equation [Ref. [2], p.13]: where λ is the wavelength of illuminating light, f and D are the focal length and aperture diameter of the camera imaging lens, respectively, and M is the magnification of the camera imaging system.
Effectiveness of FRCM Reinforcement Applied to Masonry Walls Subject to Axial Force and Out-Of-Plane Loads Evaluated by Experimental and Numerical Studies
Published in International Journal of Architectural Heritage, 2018
Alessandro Bellini, Andrea Incerti, Marco Bovo, Claudio Mazzotti
The side of the specimen under traction was prepared for the application of Digital Image Correlation (DIC) technique, by creating a random speckle pattern by means of a white paint and black dots, realized by using appropriate size markers. It should be noted that the choice of a suitable speckle pattern at this stage is very important to reach the required accuracy during the post-processing phase. The size of black dots was chosen in order to maximize accuracy without generating additional noise on the acquired images: small speckles of about 3–5 pixels in size (between 2.0 and 3.3 mm in real dimensions, in this case) proved to be the best choice. A stereoscopic system based on two high resolution (5 MP) digital cameras with a focal length of 23 mm, positioned with a baseline of 900 mm and with an angle of about 15º between them, was used to monitor 3D full-field surface displacements and deformations of the sample, reaching a pixel size (in real dimensions) of about 0.65 mm. A f-number (defined as the ratio of the lens focal length to the diameter of the entrance pupil) of 5.6 was chosen during image acquisition. Further details on the application of this innovative full-field optical method can be found in Mazzotti, Ferracuti, and Bellini (2015b). The application of DIC technique allowed obtaining the complete 3D displacement and strain maps of the front side of the tested specimens and not only in pre-assigned points.