|
|
| Line 1: |
Line 1: |
| {{about|optics and imaging systems|angular resolution in graph drawing|angular resolution (graph drawing)}}
| | Losing weight isn't as hard because persons create it out to be. We have all been there trying to lose those small extra pounds. For several persons it's difficult to receive to the weight that they want to be at.<br><br>To lose weight fast and easy change what you drink, I've seenpeople inside terrible physical form who would not drink anythingexcept diet coke. If you wish To lose weight nevertheless you won't stopdrinking pop then leave this page considering you're spending yourtime.<br><br>Avoid consuming cheese and butter. We will be amazed to know the amount of calories which these details have, even if they are consumed in smaller quantities. Even peanut butter is the most harmful thing for we if you would like to lose weight. Instead try opting for healthier choices like low calorie butter plus this means we will consume lesser calories.<br><br>One significant tip for losing fat naturally is to exercise everyday. Cardiovascular exercises including aerobics, swimming, jogging plus cycling ought to be completed everyday as they enable inside losing weight from all over the body. These ought to be combined with exercises aimed at a specific body piece, which improve and tone up muscles of the specific body region. Weight training, flexibility exercises and resistance training should be a piece of your exercise regimen. But, these must be undertaken just below the guidance and guidance of a trained pro. So, when you can afford, hire a trainer that would come plus teach we effective weight loss exercises. Otherwise, receive certain exercise videos within the marketplace and undertake exercises at house, watching them.<br><br>If you are measuring your protein consumption then for every pound of the bodyweight have about 0.5 grams of protein. This is [http://safedietplansforwomen.com/how-to-lose-weight-fast how to lose weight fast for women] the amount we want to help the growth of the lean muscle tissue.<br><br>These meals arrive because single servings so we eat really the proper amount to remain inside the calorie count. All you must do is warm the meal in the microwave plus enjoy. Along with removing temptation, diet plans additionally remove the difficulty associated with meal planning plus shopping when we go on a diet. Forget all the complicated stuff. Simply purchase the meals which appeal to we plus they may arrive at your door. If you don't desire to pick and choose the meals we can even allow the organization choose the meals for you so we have a balanced diet.<br><br>Drinking water enough to keep the body healthy will in turn help in the optimal working of all body processes. It usually guarantee that digestion, absorption and excretion happens inside the greatest technique inside the body plus may assist to remove all of the undigested and waste within the body. Our body is filled with harmful components plus removing them is 1 main task when struggling to get rid of fat fast. With excessive water intake, it will enable in flushing out these chemicals within the body and thus keep your body clean. This refuses to signify that you must keep drinking water alone, however, include it effectively into your fat loss diet to receive the maximum outcome from it. |
| {{Refimprove|date=January 2012}}
| |
| '''Angular resolution''', or '''spatial resolution''', describes the ability of any [[image-forming device]] such as an [[Optical telescope|optical]] or [[radio telescope]], a [[microscope]], a [[camera]], or an [[Human eye|eye]], to distinguish small details of an object, thereby making it a major determinant of [[image resolution]]. | |
| | |
| == Definition of terms ==
| |
| | |
| '''Resolving power''' is the ability of an imaging device to separate (i.e., to see as distinct) points of an object that are located at a small [[angular separation|angular distance]] or it is the power of an optical instrument to separate far away objects that are close together into individual images. The term '''[[Optical resolution|resolution]]''' or '''minimum resolvable distance''' is the minimum distance between distinguishable [[object (image processing)|objects]] in an image, although the term is loosely used by many users of microscopes and telescopes to describe resolving power. In scientific analysis, in general, the term "resolution" is used to describe the [[Accuracy and precision|precision]] with which any instrument measures and records (in an image or spectrum) any variable in the specimen or sample under study.
| |
| | |
| == Explanation ==
| |
| [[File:Airy Pattern.svg|thumb|right|Airy diffraction pattern generated by a plane wave falling on a circular aperture, such as the pupil of the [[Human eye|eye]]]]
| |
| The imaging system's resolution can be limited either by [[Optical aberration|aberration]] or by [[diffraction]] causing [[Focus (optics)|blurring]] of the image. These two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality — and subsequently the cost — of the system. On the other hand, diffraction comes from the wave nature of light and is determined by the finite aperture of the optical elements. The [[lens (optics)|lens]]' circular [[aperture]] is analogous to a two-dimensional version of the [[Slit experiment|single-slit experiment]]. [[Light]] passing through the lens [[Interference (wave propagation)|interferes]] with itself creating a ring-shape diffraction pattern, known as the [[Airy pattern]], if the [[wavefront]] of the transmitted light is taken to be spherical or plane over the exit aperture.
| |
| | |
| The interplay between diffraction and aberration can be characterised by the [[point spread function]]<!--Maybe should go after--> (PSF). The narrower the aperture of a lens the more likely the PSF is dominated by diffraction. In that case, the '''angular resolution''' of an optical system can be estimated (from the [[diameter]] of the aperture and the [[wavelength]] of the light) by the '''Rayleigh criterion''' invented by [[Lord Rayleigh]]:
| |
| | |
| Two point sources are regarded as just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other.<ref>{{cite book
| |
| | last = Born
| |
| | first = Max
| |
| | authorlink = Max Born
| |
| | last2 = Wolf
| |
| | first2 = Emil
| |
| | title = Principles of Optics
| |
| | publisher = [[Cambridge University Press]]
| |
| | date = October 1999
| |
| | location = Cambridge
| |
| | page = 461
| |
| | isbn = 0-521-64222-1}}</ref>
| |
| If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved. If one considers diffraction through a circular aperture, this translates into:
| |
| | |
| :{|
| |
| |<math> \theta = 1.220 \frac{\lambda}{D}</math> || || rowspan=4 |
| |
| where
| |
| :''θ'' is the '''angular resolution''',
| |
| :''λ'' is the [[wavelength]] of light,
| |
| :and ''D'' is the [[diameter]] of the lens' aperture.
| |
| |-
| |
| |
| |
| |}
| |
| | |
| The factor 1.220 is derived from a calculation of the position of the first dark circular ring surrounding the central [[Airy disc]] of the [[diffraction]] pattern. The calculation involves a [[Bessel function]]—1.220 is approximately the first zero of the Bessel function of the first kind, of order one (i.e., <math>J_{1}</math>), divided by [[pi|π]].
| |
| | |
| The formal Rayleigh criterion is close to the [[empirical]] resolution limit found earlier by the English astronomer [[W. R. Dawes]] who tested human observers on close binary stars of equal brightness. The result, ''θ'' = 4.56/''D'', with ''D'' in inches and ''θ'' in [[arcsecond]]s is slightly narrower than calculated with the Rayleigh criterion: A calculation using Airy discs as point spread function shows that at [[Dawes' limit]]<!-- that stub may redirect here --> there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip.<ref name="Michalet2006">{{cite journal|last1=Michalet|first1=X.|title=Using photon statistics to boost microscopy resolution|journal=Proceedings of the National Academy of Sciences|volume=103|issue=13|year=2006|pages=4797–4798|issn=0027-8424|doi=10.1073/pnas.0600808103|bibcode = 2006PNAS..103.4797M }}</ref> Modern [[image processing]] techniques including [[deconvolution]] of the point spread function allow resolution of even narrower binaries.
| |
| | |
| The angular resolution may be converted into a '''spatial resolution''', Δ''ℓ'', by multiplication of the angle (in radians) with the distance to the object. For a microscope, that distance is close to the [[focal length]] ''f'' of the [[Objective (optics)|objective]]. For this case, the Rayleigh criterion reads:
| |
| | |
| :<math> \Delta \ell = 1.220 \frac{ f \lambda}{D}</math>.
| |
| | |
| This is the size, in the imaging plane, of smallest object that the lens can resolve, and also the [[radius]] of the smallest spot to which a [[collimated]] beam of [[light]] can be focused.<ref>{{cite web |url=https://www.cvimellesgriot.com/products/Documents/TechnicalGuide/fundamental-Optics.pdf |title=Diffraction: Fraunhofer Diffraction at a Circular Aperture |accessdate=2011-07-04 |work=Melles Griot Optics Guide |publisher=Melles Griot |year=2002 }}</ref> The size is proportional to wavelength, ''λ'', and thus, for example, [[blue]] light can be focused to a smaller spot than [[red]] light. If the lens is focusing a beam of [[light]] with a finite extent (e.g., a [[laser]] beam), the value of ''D'' corresponds to the [[diameter]] of the light beam, not the lens.{{ref|GaussianNote|Note}} Since the spatial resolution is inversely proportional to ''D'', this leads to the slightly surprising result that a wide beam of light may be focused to a smaller spot than a narrow one. This result is related to the [[Fourier uncertainty principle|Fourier properties]] of a lens.
| |
| | |
| A similar result holds for a small sensor imaging a subject at infinity: The angular resolution can be converted to a spatial resolution ''on the sensor'' by using ''f'' as the distance to the image sensor; this relates the spatial resolution of the image to the [[f-number]], {{f/}}#:
| |
| :<math> \Delta \ell \approx 1.220 \frac{f \lambda}{D} = 1.22 \lambda \cdot (f/\#)</math>.
| |
| Since this is the radius of the Airy disk, the resolution is better estimated by the diameter, <math> 2.44 \lambda \cdot (f/\#)</math>
| |
| | |
| ==Specific cases==
| |
| [[Image:Diffraction limit diameter vs angular resolution.svg|thumb|Log-log plot of aperture diameter vs angular resolution at the diffraction limit for various light wavelengths compared with various astronomical instruments. For example, the blue star shows that the [[Hubble Space Telescope]] is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though normally only 60 arcsecs.]]
| |
| | |
| === Single telescope ===
| |
| | |
| Point-like sources separated by an [[angle]] smaller than the angular resolution cannot be resolved. A single optical telescope may have an angular resolution less than one [[arcsecond]], but [[astronomical seeing]] and other atmospheric effects make attaining this very hard.
| |
| | |
| The angular resolution ''R'' of a telescope can usually be approximated by
| |
| :<math>R = \frac {\lambda}{D} </math>
| |
| where
| |
| :''λ'' is the [[wavelength]] of the observed radiation
| |
| :and ''D'' is the diameter of the telescope's [[Objective (optics)|objective]].
| |
| | |
| Resulting ''R'' is in [[radian]]s. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources.
| |
| | |
| For example, in the case of yellow light with a wavelength of 580 nm, for a resolution of 0.1 arc second, we need D = 1.2 m.
| |
| | |
| This formula, for light with a wavelength of about 562 nm, is also called the [[Dawes' limit]].
| |
| | |
| === Telescope array ===
| |
| The highest angular resolutions can be achieved by arrays of telescopes called [[astronomical interferometer]]s: These instruments can achieve angular resolutions of 0.001 arcsecond at optical wavelengths, and much higher resolutions at radio wavelengths. In order to perform [[aperture synthesis|aperture synthesis imaging]], a large number of telescopes are required laid out in a 2-dimensional arrangement.
| |
| | |
| The angular resolution ''R'' of an interferometer array can usually be approximated by
| |
| :<math>R = \frac {\lambda}{B} </math>
| |
| where
| |
| :''λ'' is the [[wavelength]] of the observed radiation
| |
| :and ''B'' is the length of the maximum physical separation of the telescopes in the array, called the [[baseline (configuration management)|baseline]].
| |
| | |
| The resulting ''R'' is in [[radian]]s. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources.
| |
| | |
| For example, in order to form an image in yellow light with a wavelength of 580 nm, for a resolution of 1 milli-arcsecond, we need telescopes laid out in an array that is 120 m × 120 m.
| |
| | |
| === Microscope ===
| |
| The resolution ''R'' (here measured as a distance, not to be confused with the angular resolution of a previous subsection) depends on the [[angular aperture]] <math>\alpha</math>:
| |
| | |
| :<math>R=\frac{1.22\lambda}{\mathrm{NA}_\text{condenser} + \mathrm{NA}_\text{objective}}</math> where <math>\mathrm{NA}=\eta\sin\theta</math>.<ref>[http://www.microscopyu.com/articles/formulas/formulasresolution.html Nikon MicroscopyU: Concepts and Formulas in Microscopy: Resolution<!-- Bot generated title -->]</ref>
| |
| | |
| Here NA is the [[numerical aperture]], <math>\theta</math> is half the included angle <math>\alpha</math> of the lens, which depends on the diameter of the lens and its focal length, <math>\eta</math> is the [[refractive index]] of the medium between the lens and the specimen, and <math>\lambda</math> is the wavelength of light illuminating or emanating from (in the case of fluorescence microscopy) the sample.
| |
| | |
| It follows that the NAs of both the objective and the condenser should be as high as possible for maximum resolution. In the case that both NAs are the same, the equation may be reduced to: | |
| | |
| :<math>R=\frac{0.61\lambda}{\mathrm{NA}}\approx\frac{\lambda}{2\mathrm{NA}}</math>
| |
| | |
| The practical limit for <math>\theta</math> is about 70°. In an air objective or condenser, this gives a maximum NA of 0.95. In a high-resolution [[oil immersion objective|oil immersion lens]], the maximum NA is typically 1.45, when using immersion oil with a refractive index of 1.52. Due to these limitations, the resolution limit of a light microscope using [[visible light]] is about 200 [[nanometer|nm]]. Given that the shortest wavelength of visible light is [[Violet (color)|violet]] (<math>\lambda</math> ≈ 400 nm),
| |
| | |
| :<math>R=\frac{1.22 \times 400\,\mbox{nm}}{1.45\ +\ 0.95} = 203\,\mbox{nm}</math>
| |
| | |
| which is near 200 nm.
| |
| | |
| Oil immersion objectives can have practical difficulties due to their shallow depth of field and extremely short working distance, which calls for the use of very thin (0.17mm) cover slips, or, in an inverted microscope, thin glass-bottomed [[Petri dish]]es.
| |
| | |
| However, resolution below this theoretical limit can be achieved using optical near-fields ([[Near-field scanning optical microscope]]) or a diffraction technique called [[4Pi STED microscopy]]. Objects as small as 30 nm have been resolved with both techniques.<ref name=pohl>{{cite journal|author=D.W. Pohl, W. Denk, and M. Lanz|title=Optical stethoscopy: Image recording with resolution λ/20|journal=Appl. Phys. Lett.|volume=44|page=651|year=1984 |doi=10.1063/1.94865|issue=7|bibcode = 1984ApPhL..44..651P }}</ref> <ref>http://www.mpibpc.mpg.de/groups/hell/4Pi-STED.htm</ref>
| |
| | |
| == Notes ==
| |
| In the case of laser beams, a [[Gaussian beam|Gaussian Optics]] analysis is more appropriate than the Rayleigh criterion, and may reveal a smaller diffraction-limited spot size than that indicated by the formula above.
| |
| | |
| == See also ==
| |
| *[[Diffraction-limited system]]
| |
| *[[Angular diameter]]
| |
| *[[Dawes limit]]
| |
| *[[Sparrow's resolution limit]]
| |
| *[[Visual acuity]]
| |
| | |
| == References ==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| * [http://www.microscopyu.com/articles/formulas/formulasresolution.html "Concepts and Formulas in Microscopy: Resolution"] by Michael W. Davidson, ''Nikon MicroscopyU'' (website).
| |
| * Melles Griot Technical Guide: [http://cvimellesgriot.com/Products/Documents/TechnicalGuide/Fundamental-Optics.pdf Fundamental Optics].
| |
| * Melles Griot Technical Guide: [http://cvimellesgriot.com/Products/Documents/TechnicalGuide/Gaussian-Beam-Optics.pdf Gaussian Beam Optics].
| |
| | |
| [[Category:Optics]]
| |
| [[Category:Angle]]
| |
Losing weight isn't as hard because persons create it out to be. We have all been there trying to lose those small extra pounds. For several persons it's difficult to receive to the weight that they want to be at.
To lose weight fast and easy change what you drink, I've seenpeople inside terrible physical form who would not drink anythingexcept diet coke. If you wish To lose weight nevertheless you won't stopdrinking pop then leave this page considering you're spending yourtime.
Avoid consuming cheese and butter. We will be amazed to know the amount of calories which these details have, even if they are consumed in smaller quantities. Even peanut butter is the most harmful thing for we if you would like to lose weight. Instead try opting for healthier choices like low calorie butter plus this means we will consume lesser calories.
One significant tip for losing fat naturally is to exercise everyday. Cardiovascular exercises including aerobics, swimming, jogging plus cycling ought to be completed everyday as they enable inside losing weight from all over the body. These ought to be combined with exercises aimed at a specific body piece, which improve and tone up muscles of the specific body region. Weight training, flexibility exercises and resistance training should be a piece of your exercise regimen. But, these must be undertaken just below the guidance and guidance of a trained pro. So, when you can afford, hire a trainer that would come plus teach we effective weight loss exercises. Otherwise, receive certain exercise videos within the marketplace and undertake exercises at house, watching them.
If you are measuring your protein consumption then for every pound of the bodyweight have about 0.5 grams of protein. This is how to lose weight fast for women the amount we want to help the growth of the lean muscle tissue.
These meals arrive because single servings so we eat really the proper amount to remain inside the calorie count. All you must do is warm the meal in the microwave plus enjoy. Along with removing temptation, diet plans additionally remove the difficulty associated with meal planning plus shopping when we go on a diet. Forget all the complicated stuff. Simply purchase the meals which appeal to we plus they may arrive at your door. If you don't desire to pick and choose the meals we can even allow the organization choose the meals for you so we have a balanced diet.
Drinking water enough to keep the body healthy will in turn help in the optimal working of all body processes. It usually guarantee that digestion, absorption and excretion happens inside the greatest technique inside the body plus may assist to remove all of the undigested and waste within the body. Our body is filled with harmful components plus removing them is 1 main task when struggling to get rid of fat fast. With excessive water intake, it will enable in flushing out these chemicals within the body and thus keep your body clean. This refuses to signify that you must keep drinking water alone, however, include it effectively into your fat loss diet to receive the maximum outcome from it.