Limits of Resolution: The Rayleigh Criterion
The Rayleigh criterion stated in the equation = 1 22 D gives the smallest possible angle between point sources, or the best obtainable resolution Once this angle is found, the distance between stars can be calculated, since we are given how far away they are Solution for (a) The Rayleigh criterion for the minimum resolvable angle is = 1 22 D: (2)
Rayleigh’s criterion
minimum of the diffraction pattern of the other, a condition called Rayleigh’s criterion for resolvability From Eq 36-12, two objects that are barely resolvable by this criterion must have an angular separation u R of Since the angles are small,we can replace sin u R with u R expressed in radians: (Rayleigh’s criterion) (36-14) Human Vision
Resolution - Massachusetts Institute of Technology
The two–point resolution problem object: two point sources, mutually incoherent (e g two stars in the night sky; two fluorescent beads in a solution) x x′ imaging system intensity pattern observed (e g with digital camera) The resolution question [Rayleigh, 1879]: when do we cease to be able to resolve the two point sources (i e , tell
Rayleigh’s Criterion and Resolving Power of Grating
The Rayleigh Criterion The Rayleigh criterion is the generally accepted criterion for the minimum resolvable detail - the imaging process is said to be diffraction-limited when the first diffraction minimum of the image of one source point coincides with the maximum of another
Resolution - Lithoguru
Rayleigh criterion becomes less accurate at predicting the influence of NA on resolution Resolution is a fundamental measure of the capability of a lithography process By applying the rigorous definition of resolution given here, resolution can be measured and used to quantify the impact
Lecture today: Chapter 36 (finish diffraction) 1) Diffraction
Rayleigh’s criterion for resolvability Two objects that are barely resolvable by this criterion must have an angular separation θ R = 1 22 λ/d Note: - The resolution is limited by the aperture diameter d To get a good resolution or small θ R we need d to be LARGE - The resolution is a function of the wavelength
Lecture 5 - UIUC
of resolution 0 I I0 α=αc/3 Sum 2I0 0 y Two images not resolvable α D α Two point sources Rayleigh’s Criterion defines the images to be resolved if the central maximum of one image falls on or further than the first minimum of the second image c D λ α= 1 22 NOTE: No interference Why not? Angular Resolution
Understanding Resolution - Cloudy Nights
the light observed Resolution is independent of focal length or magnification, however it is dependant on the magnitude and color of the stars observed In telescopes we use the angular value for resolution, usually reported in arc seconds Suiter: fiThe Rayleigh resolution criterion is met when the separation of the two objects is precisely
Two-Point Resolution capabilities for an optical system with
Rayleigh and Sparrow criteria were modified to suit various imaging situations, CHATURVEDI and SODHA [9], ASAKURA [4], JAISWAL and BHOGRA [10], BHATNAGAR, SIROHI and SHARMA [5], etc CARSWELL and RICHARD [11] suggested a criterion for coherent system as an extension of Rayleigh criterion The two-point resolution studies for one-
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MIT 2.71/2.710 Optics
11/23/05 wk12-b-1
Resolution
MIT 2.71/2.710 Optics
11/23/05 wk12-b-2
The meaning of "resolution"
[from the New Merriam-Webster Dictionary, 1989 ed.]: resolvev: 1to break up into constituent parts: ANALYZE;2to find an answer to : SOLVE; 3DETERMINE, DECIDE;
4to make or pass a formal resolution
resolutionn: 1the act or process of resolving 2the action of solving, also: SOLUTION; 3the quality of being resolute :FIRMNESS, DETERMINATION; 4a formal statement
expressing the opinion, will or, intent of a body of personsMIT 2.71/2.710 Optics
11/23/05 wk12-b-3
The two-point resolution problem
object: two point sources, mutually incoherent (e.g. two stars in the night sky; two fluorescent beads in a solution) x x imaging systemintensity pattern observed (e.g. with digital camera)The resolution question
[Rayleigh, 1879]: when do we cease to be able to resolve the two point sources (i.e., tell them apart) due to the blurring introduced in the image by the finite (NA)?MIT 2.71/2.710 Optics
11/23/05 wk12-b-4
Numerical Aperture and Speed (or F-Number)
medium of refr. index nș: half-angle subtended by the
imaging system from an axialobjectNumerical Aperture
(NA) = nsinșSpeed(f/#)=1/2(NA)pronounced f-number, e.g.
f/8 means (f/#)=8.Aperture stopthe physical element which limits the angle of acceptance of the imaging systemMIT 2.71/2.710 Optics
11/23/05 wk12-b-5
yxyxg in OSO Sr fRr fR 11 1 22J2.,.jinc
object plane impulseFourier plane
circ-apertureimage plane observed field (PSF) 1 f 1 f cc ccccRryxHcirc, monochromatic coherent on-axis illuminationFourier
transform x x x 1 f 1 f radial coordinate @ Fourier plane 22yxr 22
yxr radial coordinate @ image plane (unit magnification) 2R