In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.An image-forming optical system with aberration will produce an image which is not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration.
Aberration can be analyzed with the techniques of geometrical optics. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays.
A large disk rotates at uniform angular speed ##\Omega## in an inertial frame ##S##. Two observers, ##O_1## and ##O_2##, ride on the disk at radial distances ##r_1## and ##r_2##, respectively, from the center (not necessarily on the same radial line). They carry clocks, ##C_1## and ##C_2##...
I am using 2 lenses in a 4f configuration. The input is a large collimated beam (632nm). After passage through the 2 lenses the beams vertical dimension remains constant, however, the horizontal dimension get smaller, as if it is being focused only in the horizontal direction. Does anyone have...
I was recently looking for proven relations between focal length, radius of curvature, refractive index etc of a convex lens as I was working on an experiment, I did Find a relation, between Height from principal axis and focal length, and it was a huge relation!I did the experiment to verify...
Is there any formula or a mathematical relation to find aberration in lenses? I read recently that plano concave lens has a negative aberration and plano convex lens is used to correct it. I am not sure what those statements mean. Is there some type of relation that explains these statements or...
I wanted to know about spherical aberration in a biconvex and plano convex lens as I was planning an experiment with them.
I was reading about them and came upon the following passage.
I don't know whether the given equation is an empirical one or a derived equation.
Can anyone help me if you...
I believe I have understood the formula of aberration of light ##\tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} \sqrt{1-\beta^{2}} ##
but I wonder if the non-relativistic formula ## \tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} ## has a physical relevance. Does this...
Hello, everyone. I am trying to find an aberration of light formula in Einstein's writings that is given in terms of tangents. I did a fairly thorough internet search and all I could find was the formula he wrote in terms of cosines. Yet I have a vague memory that somewhere he did give the...
Simple as it sounds!
Usually people derive aberration of light using linear motion, not circular motion. When aberration happens in linear motion, one would expect distance between the source and the observer to change. But, in circular motion, the path light takes in the circular motion, in...
Hello, i wear glasses (i have 2 pairs) ones are 1.60 esseilor (-4.50 and -4.75) cylinder 0,25 both and new ones that i got yesterday Trivex perfalit 1.53 (-5.00 and -4.75) cylinder 0,25 both.(+ antireflex both) And the problem with first ones was from center i see ok but when i look at the...
Leitz Summicron 50 is one of the extremelly well corrected lens in the world. Legend says about this lenses internal elements and their spherical aberrations was responsible of lot of beatiful effects on image.
For highly corrected lens image , does high internal aberration really effects the...
I am working through "Spacetime Physics" and encountered exercise 3-9, which concerns aberration of starlight. They ask the following question: "Since the background of stars also shifts due to aberration, how can the effect be measured at all?"
I got part of the answer. You measure the angle...
Homework Statement
Derive an analytic expression for the distance from the vertex to the focus for a particular ray in terms of (i) the radius of curvature R of the concave mirror (ii) the angle of incidence θ between incident ray and radius of the mirror. Hence show that the focus moves closer...
I was studyng my exam of astrophysics laboratory, while treathing the optical aberration I've wondered: does radio telescope have aberration? Is a paraboloid antenna in a single dish affected by coma? and the radio telescope made by arrays of resonant structures?
Maybe those are silly...
The rays of light from a moving source are tilted towards the direction of the source's motion. It is as if light emitted by a moving object is concentrated conically, towards its direction of motion. This effect is called relativistic beaming.
For example, if a source is emitting light...
Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z.
However, because of relativistic aberration the two light rays will make...
In 1727, astronomer J. Bradley discovered the phenomenon of stellar aberration. All stars throughout the year on the celestial sphere pass ellipses with an semimajor axis observed from the Earth at an angle of 20.5. Aberration is caused by the movement of the Earth in its orbit around the sun at...
Homework Statement
So the problem is the following : we observe the stellar aberration of a star which isn't on the zenith, so that the star forms an angle theta with the ecliptic plane of the Earth. With such a position, the star will describe an ellipse instead of a circle (typical movement...
Homework Statement
A particle has speed u‘ in the S’ frame, its track making an angle ## \theta’ ## with the x’ axis. The particle is viewed by an observer in frame S, the two frames having a relative speed parameter ## \beta ##.
(a) Show that the angle ## \theta ## made by the track of the...
Hi there,
optical aberrations can be expressed by Zernike polynomials Vmn(ρ,θ).
Now, for my simulations i am using software that takes 4 inputs for creating aberrations onto an optical flat: m,n,R,A
m,n are the Zernike orders which is perfectly clear.
For R,A the manual says:
R: the radius
A...
Hi, I have 2 similar lens systems used for basic astronomy (as refracting telescopes). The first is a telephoto lens designed for a camera and the second is the main objective of an old pair of binocs paired with an eyepiece in a tube. I am suspecting the former exhibits more chromatic...
Flying two aircraft (parallel and synchronous).
From the first emitted light beam. As this beam reaches the second plane?
Perpendicular (FIG. 1), or with a bend (FIG. 2)?
Not sure if this will be of interest to others, but, as an exercise, I decided to derive formulas for SR velocity addition for any angular relationship, and similar aberration of angle for any object speed and direction and observer relative velocity - using pure algebra/geometry. That is, no...
I have been coding a speed of light simulator and I am having a bit of trouble with a few aspects of the project. My first question is:
Are the length contraction and relativistic aberration formulas BOTH needed in my calculations or does the relativistic aberration formula already account for...
Hi everyone,
I am interested in measuring stellar aberration as a challenge to myself; I am more of a physicist than an astronomer. I have a fair knowledge of telescopes and imaging. I would appreciate if somebody can give me instructions or point to some references on: which star to select...
Let S be the frame where the Sun is at rest. Imagine light from the North Star reaches the centre of the Sun, and let's define the equatorial plane as the plane that is perpendicular to this light and cuts the Sun into two hemisphere.
Suppose a distant star A is on this equatorial plane and its...
I am trying to model a simple system, but the ray-tracing does not seem to be consistent with the analysis of the system in terms of Seidel aberration values. Here's the system layout:
When the system contains only the Eye model and the OL lens, it can be referred from the Seidel diagram that...
Homework Statement
Estimate the size of the spherical abberation of a spherical mirror of 1m-diameter and a focal
length of 2 meter. (Hint: Calculate the size of the smeared image of a star at the focal point and compare it to the size (in arc-sec) of an extended object)Homework Equations
The...
The Lorentz's transform:
##x' = k(x - vt), t' = k(t - vx)\ k = \gamma,\ and\ c = 1##
I. The speed composition derivation:
##w' = dx'/dt' = \frac{dx - vdt}{dt - vdx}##
and we divide everything by dt, and:
##w' = \frac{dx/dt - v}{1 - vdx/dt}##
now we assume the dx/dt is some speed u, and the...
In an inertial reference frame - and zero gravity field - we believe that any passing photons go in Euclidean straight lines. If I have some constant velocity towards the path of a passing photon, it still goes in a straight line, just at a different angle. But if I am accelerating towards that...
I thought I understood how stellar aberration conformed to Special Relativity. The CHANGE in that angle comes from the CHANGE in our orbital velocity direction about the sun over six months. And it is the same for all stars. That is fine if there are no significant changes in a star’s state of...
Homework Statement
http://s22.postimg.org/5vp0p2aox/Untitled.png [Broken]
Homework Equations
The Attempt at a Solution
Here is the solution
I understand everything that must be done after one find the correct transformations for the two coordinates, but I don't understand why...
Hi everybody, I really need help and it's quite an emergency..
I have this problem to do but I'm really stuck I don't know where I have to begin and I don't even understand what they're asking for:
A star in the sky is observed from Earth to describe an elliptical path whose minor axis subtends...
Hi there,
I'm having a little confusion regarding spherical aberration from some experiments I've been doing with a concave mirror. I've been directing the mirror so that it faces the distance (ie. objects at infinity) and then positioning a flat piece of paper so that an image forms on it. The...
I'm reading Eisenstaedt, The curious history of relativity: how Einstein's theory of gravity was lost and found again. In ch. 1, Eisenstaedt says that in the early 18th century, James Bradley at Oxford tried to observe parallax, failed, but detected a much larger effect, aberration, which showed...
Q: Consider your own eyesight. Can you detect any indication of spherical aberration? If so, describe what you see.
A: I understand spherical aberration is generated by spherical lenses or mirrors and causes light to spread, which results in a blurry image. My initial thought was yes, a...
Homework Statement
Hi, I have a question regarding my physics lab assignment. Last week I performed an experiment on the focal length of a biconcave lens using different part (using the radius of the lens) of the lens. This is done by completely covering the lens with a cardboard except for...
At another thread under Special and General Relativity the following question was asked:
"Why isn't stellar aberration considered to be a one way measurement of c?
If the angle of aberration (θ-θ0) is -20.5 arc seconds and the Earth's orbital speed is 29.79 Kilometers/second normal to the...
Does relativistic aberration apply to electric fields and magnetic fields? If a spaceship accelerated to a relativistic speed with respect to an initial inertial frame, in a constant direction with respect to a uniform electric field, do the effects of aberration affect the magnitude of electric...
i need someone to explain me the aberration of light , i tried to read i from my book its a bit more complicated than i thought i mean when we move the microcope we make a tilt what do you mean by that?
all in all i didnt understand this concept and i need a really clear explanation especially...
I know that a spherical lens does indeed have spherical aberration, and I know that this is caused by the marginal and axel rays of light converging at different points. My question is why? What is it about the lens that makes the rays incedent on the edges of the lens focus at a closer point...
hi everybody,
i would appreciate it if someone could clarify the concept of spherical aberrations in the context of high NA objectives in which use lenses are used that are not exclusively of the spherical type.
a common thing that you hear is that some objective is corrected for 0.17mm...
Aberration of starlight due to...
I have read that the 20+ arcsec annual aberration of starlight is explained by special relativity, but I found no further comment.
So how is it explained in SR?
-HarryWertm
I've been puzzled by this. If light of different frequencies (like ultra violet to infra-red) would experience different refraction angles in the presence of a powerful gravity field. I understand that light has zero rest mass but has effective mass given the fact it's in motion.
What I'm...
I have been reading in my book on Special Relativity (A. P. French, Chapman & Hall) that stellar abberation as discovered by Bradley, only made sense to physicists at the time in the context of a wave/ether model of the propagation of light IF the Earth moved with respect to the ether.
I don't...
As I was studying Comatic aberration, in the definition of coma the word off-axis is used which I couldnot understand. What does off axis means? and how does it contribute to the comatic aberration? I also want to know about off axis diagrammatically.Thanks......
Homework Statement
- single lens
- f=50cm
- refractive index n=1.53
- if object placed 70cm, find the radii of curvature for the two surfaces of the lens which would minimise spehrical aberrationHomework Equations
what i got from my notes
refraction at a spherical surface...
I'm trying to construct a lens model, and having trouble because I want to portray a perfect lens rather than one with spherical aberration. It's proved impossible to find via Google, although I did find an earlier thread on this forum that was helpful.
From what I can gather, the lens needs...
Sorry for posting this post in two different place, I could not decide where is the best place to post it.
I am trying to build a Galilean beam expander/contraction using a plano-convex and plano-convace lenses. My question is how should I arrange them to reduce the spherical aberration...