In optics, an aperture is a hole or an opening through which light travels. More the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An optical system has many openings or structures that limit the ray bundles; these structures may be the edge of a lens or mirror, or a ring or other fixture that holds an optical element in place, or may be a special element such as a diaphragm placed in the optical path to limit the light admitted by the system. In general, these structures are called stops, the aperture stop is the stop that determines the ray cone angle and brightness at the image point. In some contexts in photography and astronomy, aperture refers to the diameter of the aperture stop rather than the physical stop or the opening itself. For example, in a telescope, the aperture stop is the edges of the objective lens or mirror. One speaks of a telescope as having, for example, a 100-centimeter aperture. Note that the aperture stop is not the smallest stop in the system.

Magnification and demagnification by lenses and other elements can cause a large stop to be the aperture stop for the system. In astrophotography, the aperture may be given as a linear measure or as the dimensionless ratio between that measure and the focal length. In other photography, it is given as a ratio. Sometimes stops and diaphragms are called apertures when they are not the aperture stop of the system; the word aperture is used in other contexts to indicate a system which blocks off light outside a certain region. In astronomy, for example, a photometric aperture around a star corresponds to a circular window around the image of a star within which the light intensity is assumed; the aperture stop is an important element in most optical designs. Its most obvious feature is; this can be either unavoidable, as in a telescope where one wants to collect as much light as possible. In both cases, the size of the aperture stop is constrained by things other than the amount of light admitted. Smaller stops produce a longer depth of field, allowing objects at a wide range of distances from the viewer to all be in focus at the same time.

The stop limits the effect of optical aberrations. If the stop is too large, the image will be distorted. More sophisticated optical system designs can mitigate the effect of aberrations, allowing a larger stop and therefore greater light collecting ability; the stop determines. Larger stops can cause the intensity reaching the film or detector to fall off toward the edges of the picture when, for off-axis points, a different stop becomes the aperture stop by virtue of cutting off more light than did the stop, the aperture stop on the optic axis. A larger aperture stop requires larger diameter optics, which are more expensive. In addition to an aperture stop, a photographic lens may have one or more field stops, which limit the system's field of view; when the field of view is limited by a field stop in the lens vignetting results. The biological pupil of the eye is its aperture in optics nomenclature. Refraction in the cornea causes the effective aperture to differ from the physical pupil diameter.

The entrance pupil is about 4 mm in diameter, although it can range from 2 mm in a brightly lit place to 8 mm in the dark. In astronomy, the diameter of the aperture stop is a critical parameter in the design of a telescope. One would want the aperture to be as large as possible, to collect the maximum amount of light from the distant objects being imaged; the size of the aperture is limited, however, in practice by considerations of cost and weight, as well as prevention of aberrations. Apertures are used in laser energy control, close aperture z-scan technique, diffractions/patterns, beam cleaning. Laser applications include Q-switching, high intensity x-ray control. In light microscopy, the word aperture may be used with reference to either the condenser, field iris or objective lens. See Optical microscope; the aperture stop of a photographic lens can be adjusted to control the amount of light reaching the film or image sensor. In combination with variation of shutter speed, the aperture size will regulate the film's or image sensor's degree of exposure to light.

A fast shutter will require a larger aperture to ensure sufficient light exposure, a slow shutter will require a smaller aperture to avoid excessive exposure. A device called a diaphragm serves as the aperture stop, controls the aperture; the diaphragm functions much like the iris of the eye – it controls the effective diameter of the lens opening. Reducing the aperture size increases the depth of field, which describes the extent to which subject matter lying closer than or farther from the actual plane of focus appears to be in focus. In general, the smaller the aperture, the greater the distance from the plane of focus the subject ma

Polynomial regression

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E. Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression; the explanatory variables resulting from the polynomial expansion of the "baseline" variables are known as higher-degree terms. Such variables are used in classification settings. Polynomial regression models are fit using the method of least squares; the least-squares method minimizes the variance of the unbiased estimators of the coefficients, under the conditions of the Gauss–Markov theorem.

The least-squares method was published in 1805 in 1809 by Gauss. The first design of an experiment for polynomial regression appeared in an 1815 paper of Gergonne. In the twentieth century, polynomial regression played an important role in the development of regression analysis, with a greater emphasis on issues of design and inference. More the use of polynomial models has been complemented by other methods, with non-polynomial models having advantages for some classes of problems; the goal of regression analysis is to model the expected value of a dependent variable y in terms of the value of an independent variable x. In simple linear regression, the model y = β 0 + β 1 x + ε, is used, where ε is an unobserved random error with mean zero conditioned on a scalar variable x. In this model, for each unit increase in the value of x, the conditional expectation of y increases by β1 units. In many settings, such a linear relationship may not hold. For example, if we are modeling the yield of a chemical synthesis in terms of the temperature at which the synthesis takes place, we may find that the yield improves by increasing amounts for each unit increase in temperature.

In this case, we might propose a quadratic model of the form y = β 0 + β 1 x + β 2 x 2 + ε. In this model, when the temperature is increased from x to x + 1 units, the expected yield changes by β 1 + β 2. For infinitesimal changes in x, the effect on y is given by the total derivative with respect to x: β 1 + 2 β 2 x; the fact that the change in yield depends on x is what makes the relationship between x and y nonlinear though the model is linear in the parameters to be estimated. In general, we can model the expected value of y as an nth degree polynomial, yielding the general polynomial regression model y = β 0 + β 1 x + β 2 x 2 + β 3 x 3 + ⋯ + β n x n + ε. Conveniently, these models are all linear from the point of view of estimation, since the regression function is linear in terms of the unknown parameters β0, β1.... Therefore, for least squares analysis, the computational and inferential problems of polynomial regression can be addressed using the techniques of multiple regression; this is done by treating x, x2... as being distinct independent variables in a multiple regression model.

The polynomial regression model y i = β 0 + β 1 x i + β 2 x i 2 + ⋯ + β m x i m + ε i can be expressed in matrix form in terms of a design matrix X, a response vector y →, a parameter vector β →, a vector ε → of random errors. The i-th row of X and y → will contain the x and y value for the i-th data sample; the model can be written as a system of linear equations: [


Peralasseri is a census town in Kannur district in the Indian state of Kerala, situated on the Kannur-Kuthuparamba high road 12 km from Kannur town, on the bank of Anjarakandy river. Peralasseri is 15 kilometres from the district headquarters Kannur; the nearest town and railway stations are Thalassery, 14 km and Kannur which is15 km away. The Place is surrounded by 4 panchayats: Kadambur, Anjarakandi, Pinarayi; the Panchayath Office is located near Peralassery Subrahmanya Temple. As of 2001 India census, Peralasseri had a population of 15,818. Males constitute 47% of the population and females 53%. Peralasseri has an average literacy rate of 86%, higher than the national average of 59.5%: male literacy is 88%, female literacy is 85%. In Peralasseri, 10% of the population is under 6 years of age; this is one of the smallest towns in kannur district of kerala state. Kannur - Kuthuparamba state highway is passing through this place. Peralasseri is about 14 km away from the proposed Kannur airport; the hanging bridge of Peralasseri is a notable tourist attraction.

Built across the Anjarakandy river, this is one of the few hanging bridges in Kannur district. Peralassery Grama Panchayath Office Mundaloor Post office Makreri Village Office KSEB Electrical Section Office - Peralassery Kerala Water Authority Asst Engineer Office and Asst Executive Engineer Office. BSNL Telephone Exchange - Peralassery Peralasseri A. K. G. Smaraka Govt. Higher Secondary School is an old school of Peralasseri town; the school is situated near the Peralasseri Temple at Mundalloor on the Kannur road. The school is known for good results and one of the good government school in Kerala AKG Smaraka Co- op hospital Govt. Ayurvedic Dispensary AKG Smaraka Govt. Higher secondary school Peralasseri Service Co-op Bank - Main Branch Central Bank Of India - Peralasseri Branch Mownachery Co-op Rural Bank - Peralasseri Branch Canara Bank - Peralasseri Branch Peralasseri Subrahmanya Temple Peralasseri Naroth Mahavishnu Temple Rangoth Bhagavathy Temple Makrery Subrahmanya-Hanuman Temple Mahavishnu Sivakshetram Aivarkulam Mundaloor Rifayi Masjid AKG vaayanashala Mundaloor Mueenul Islam Sabha Secondary Madrassa.

Peralassery Markaz Yatheem Khana Chirathukandi Azhikkodan club AKG Memorial Raidco Curry Powder Factory - Mo Peralasseri Panchayath Mini Industrial Estate The national highway passes through Kannur town. Goa and Mumbai can be accessed on the northern side and Cochin and Thiruvananthapuram can be accessed on the southern side; the road to the east of Iritty connects to Bangalore. The nearest railway station is Kannur on Mangalore-Palakkad line. Trains are available to all parts of India subject to advance booking over the internet. There are airports at Mattanur and Calicut. All of them are international airports but direct flights are available only to Middle Eastern countries. A K Gopalan - Politician, Social Reformer C. H Kunjappa - Writer Sukala Suresh - Artist