 | This article may be confusing or unclear to readers.(May 2010) |
In signal processing, apodization (from Greek "removing the foot") is the modification of the shape of a mathematical function. The function may represent an electrical signal, an optical transmission, or a mechanical structure. In optics, it is primarily used to remove Airy disks caused by diffraction around an intensity peak, improving the focus.
The term apodization is used frequently in publications on Fourier-transform infrared (FTIR) signal processing. An example of apodization is the use of the Hann window in the fast Fourier transform analyzer to smooth the discontinuities at the beginning and end of the sampled time record.
An apodizing filter can be used in digital audio processing instead of the more common brick-wall filters, in order to reduce the pre- and post-ringing that the latter introduces. [1]
During oscillation within an Orbitrap, ion transient signal may not be stable until the ions settle into their oscillations. Toward the end, subtle ion collisions have added up to cause noticeable dephasing. This presents a problem for the Fourier transformation, as it averages the oscillatory signal across the length of the time-domain measurement. The software allows “apodization”, the removal of the front and back section of the transient signal from consideration in the FT calculation. Thus, apodization improves the resolution of the resulting mass spectrum. Another way to improve the quality of the transient is to wait to collect data until ions have settled into stable oscillatory motion within the trap. [2]
Apodization is applied to NMR signals before discrete Fourier Transformation. Typically, NMR signals are truncated due to time constraints (indirect dimension) or to obtain a higher signal-to-noise ratio. In order to reduce truncation artifacts, the signals are subjected to apodization with different types of window functions. [3]
In optical design jargon, an apodization function is used to purposely change the input intensity profile of an optical system, and it may be a complicated function to tailor the system to certain properties. Usually, it refers to a non-uniform illumination or transmission profile that approaches zero at the edges.
Since side lobes of the Airy disk are responsible for degrading the image, techniques for suppressing them are utilized. If the imaging beam has Gaussian distribution, when the truncation ratio (the ratio of the diameter of the Gaussian beam to the diameter of the truncating aperture) is set to 1, the side-lobes become negligible and the beam profile becomes purely Gaussian. [4] [ page needed ]
In medical ultrasonography, the effect of grating lobes can be reduced by activating ultrasonic transducer elements using variable voltages in apodization process. [5]
Most camera lenses contain diaphragms which decrease the amount of light coming into the camera. These are not strictly an example of apodization, since the diaphragm does not produce a smooth transition to zero intensity, nor does it provide shaping of the intensity profile (beyond the obvious all-or-nothing, "top hat" transmission of its aperture).
Some lenses use other methods to reduce the amount of light let in. For example, the Minolta/Sony STF 135mm f/2.8 T4.5 lens however, has a special design introduced in 1999, which accomplishes this by utilizing a concave neutral-gray tinted lens element as an apodization filter, thereby producing a pleasant bokeh. The same optical effect can be achieved by combining depth-of-field bracketing with multi exposure, as implemented in the Minolta Maxxum 7's STF function. In 2014, Fujifilm announced a lens utilizing a similar apodization filter in the Fujinon XF 56mm F1.2 R APD lens. [6] In 2017, Sony introduced the E-mount full-frame lens Sony FE 100mm F2.8 STF GM OSS (SEL-100F28GM) based on the same optical Smooth Trans Focus principle. [7]
Simulation of a Gaussian laser beam input profile is also an example of apodization.[ citation needed ]
Photon sieves provide a relatively easy way to achieve tailored optical apodization. [8]
Apodization is used in telescope optics in order to improve the dynamic range of the image. For example, stars with low intensity in the close vicinity of very bright stars can be made visible using this technique, and even images of planets can be obtained when otherwise obscured by the bright atmosphere of the star they orbit. [9] [10] [11] Generally, apodization reduces the resolution of an optical image; however because it reduces diffraction edge effects, it can actually enhance certain small details. In fact, the notion of resolution, as it is commonly defined with the Rayleigh criterion, is in this case partially irrelevant. One has to understand that the image formed in the focal plane of a lens (or a mirror) is modeled through the Fresnel diffraction formalism. The classical diffraction pattern, the Airy disk, is connected to a circular pupil, without any obstruction, and with a uniform transmission. Any change in the shape of the pupil (for example a square instead of a circle), or its transmission, results in an alteration in the associated diffraction pattern.
Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
Microscopy is the technical field of using microscopes to view objects and areas of objects that cannot be seen with the naked eye. There are three well-known branches of microscopy: optical, electron, and scanning probe microscopy, along with the emerging field of X-ray microscopy.
In photography, bokeh is the aesthetic quality of the blur produced in out-of-focus parts of an image, whether foreground or background or both. It is created by using a wide aperture lens.
Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. It is used in optics applied to light waves, in antenna theory applied to radio waves, and in acoustics applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, θ, which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term spatial resolution refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image-forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high-resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes have large apertures.
Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or superposition, of plane waves. It has some parallels to the Huygens–Fresnel principle, in which the wavefront is regarded as being made up of a combination of spherical wavefronts whose sum is the wavefront being studied. A key difference is that Fourier optics considers the plane waves to be natural modes of the propagation medium, as opposed to Huygens–Fresnel, where the spherical waves originate in the physical medium.
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.
In optics, any optical instrument or system – a microscope, telescope, or camera – has a principal limit to its resolution due to the physics of diffraction. An optical instrument is said to be diffraction-limited if it has reached this limit of resolution performance. Other factors may affect an optical system's performance, such as lens imperfections or aberrations, but these are caused by errors in the manufacture or calculation of a lens, whereas the diffraction limit is the maximum resolution possible for a theoretically perfect, or ideal, optical system.
In optics, the Airy disk and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, optics, and astronomy.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance from the object, and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object and is given by the Fresnel diffraction equation.
The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system. The PSF in many contexts can be thought of as the extended blob in an image that represents a single point object, that is considered as a spatial impulse. In functional terms, it is the spatial domain version of the optical transfer function (OTF) of an imaging system. It is a useful concept in Fourier optics, astronomical imaging, medical imaging, electron microscopy and other imaging techniques such as 3D microscopy and fluorescence microscopy.
A spatial filter is an optical device which uses the principles of Fourier optics to alter the structure of a beam of light or other electromagnetic radiation, typically coherent laser light. Spatial filtering is commonly used to "clean up" the output of lasers, removing aberrations in the beam due to imperfect, dirty, or damaged optics, or due to variations in the laser gain medium itself. This filtering can be applied to transmit a pure transverse mode from a multimode laser while blocking other modes emitted from the optical resonator. The term "filtering" indicates that the desirable structural features of the original source pass through the filter, while the undesirable features are blocked. An apparatus which follows the filter effectively sees a higher-quality but lower-powered image of the source, instead of the actual source directly. An example of the use of spatial filter can be seen in advanced setup of micro-Raman spectroscopy.
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are captured or transmitted. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain. A variant, the modulation transfer function (MTF), neglects phase effects, but is equivalent to the OTF in many situations.
The Strehl ratio is a measure of the quality of optical image formation, originally proposed by Karl Strehl, after whom the term is named. Used variously in situations where optical resolution is compromised due to lens aberrations or due to imaging through the turbulent atmosphere, the Strehl ratio has a value between 0 and 1, with a hypothetical, perfectly unaberrated optical system having a Strehl ratio of 1.
Originally produced by Minolta, and currently produced by Sony, the STF 135mm f/2.8 [T4.5] is a photographic lens compatible with cameras using the Minolta AF and Sony α A-mount. STF stands for Smooth Trans Focus, in reference to its special optical system, which is intended to smooth the transition between the plane of focus and out-of-focus areas in the image. This is accomplished by the use of an apodization filter that provides the high-quality bokeh effect. The lens is not a soft-focus lens.
A point diffraction interferometer (PDI) is a type of common-path interferometer. Unlike an amplitude-splitting interferometer, such as a Michelson interferometer, which separates out an unaberrated beam and interferes this with the test beam, a common-path interferometer generates its own reference beam. In PDI systems, the test and reference beams travel the same or almost the same path. This design makes the PDI extremely useful when environmental isolation is not possible or a reduction in the number of precision optics is required. The reference beam is created from a portion of the test beam by diffraction from a small pinhole in a semitransparent coating. The principle of a PDI is shown in Figure 1.
A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers—ultraviolet, visible, infrared, continuous wave, pulsed, high-power, low-power—there is an assortment of instrumentation for measuring laser beam profiles. No single laser beam profiler can handle every power level, pulse duration, repetition rate, wavelength, and beam size.
In signal processing, particularly digital image processing, ringing artifacts are artifacts that appear as spurious signals near sharp transitions in a signal. Visually, they appear as bands or "ghosts" near edges; audibly, they appear as "echos" near transients, particularly sounds from percussion instruments; most noticeable are the pre-echos. The term "ringing" is because the output signal oscillates at a fading rate around a sharp transition in the input, similar to a bell after being struck. As with other artifacts, their minimization is a criterion in filter design.
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample. This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM.
The Smooth Trans Focus (STF) technology in photographic lenses uses an apodization filter to realize notably smooth bokeh with rounded out-of-focus highlights in both the foreground and background. This is accomplished by utilizing a concave neutral-gray tinted lens element next to the aperture blades as apodization filter, a technology originally invented by Minolta in the 1980s, and first implemented in a commercially available lens in 1999. In contrast to soft focus lenses, STF lenses render a perfectly sharp image in the focus plane.
The Fujinon XF 56mm F1.2 R is an interchangeable camera lens announced by Fujifilm on January 6, 2014. As of 2015, it is one of the widest-aperture native mirrorless lenses.
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