ABERRATIONS

Dr.N. LALITHA KUMARI

Lecturer in PHYSICS

Silver Jubilee Govt.,College(A),

KURNOOL

ABOUT LENS

CF2

F1 R1R2f

1

1

2

2

1---marginal rays2----paraxial rays.

Derivation produced by a thin lens

hβα

δ

co I

u vFrom the ▲AIO, δ=α+β

Hence α=tanα and β=tanβ

α= h/u and β=h/v

Now, δ=h/u + h/v since u=-ve and v=+ve

δ=h/v-h/u=h(1/v-1/u)

Or δ=h/f

ABERRATIONS Definition of Aberrations. Types of Aberrations.

Chromatic Aberrations.

Monochromatic Aberrations. Mathematical Analysis & Visuals. Methods of Elimination.

What is an Aberration?

The deviations or defects observed in the actual size, position, shape and colour in the image of an object formed by a single lens are called Aberrations.

CAUSE FOR ABERRATIONS

These aberrations are caused due to

the convergence of different rays to

different points.

TYPES OF ABERRATIONS

CHROMATIC ABERRATIONS Formation of Multicoloured image.

Disability of lens to converge different colours at different points.

TYPES OF CHROMATIC ABERRATIONS

Longitudinal The formation of images of different

colours in different positions along the axis

Lateral /Transverse The defect in images of different colours

are formed of different sizes perpendicular to the axis .

LONGITUDINAL CHROMATIC ABERRATIONS

Chromatic aberration of a single lens causes different wavelengths of light to have differing focal lengths.

L.C.A.= f r - f v

CALCUALTION OF LONFITUDINAL CHROMATIC ABERRATION OF A

THIN LENS

(i)When the object is situated at infinity.

(ii)When the object is situated at a finite distance.

General formulae=1/f=(µ-1)(1/R1-1/R2),

If fv,fR and fy be the focal length of the lens for violet, red and yellow

1/fv=(µv-1)(1/R1-1/R2), ………..(1)

1/fR=(µR-1)(1/R1-1/R2),……………(2)

1/fY=(µY-1)(1/R1-1/R2)……………….(3)

2 in 1 gives 1/fv-1/fR=(µv-µR)(1/R1-1/R2),fR-fv =(µv-µR)(µy-1)(1/R1-1/R2),

fv.fR (µy-1)

BY SOLVING THEMfR-fv=ώ.fy

WHEN THE IMAGE AT A FINITE DISTANCE THENVR-VV=ώ/fV .Vy

2

When the object is situated at infinity

LATERAL/TRANSVERSE CHROMATIC ABERRATIONS

Origin of transverse chromatic aberration. The size of the image varies from one color to the next.

Visual of chromatic aberrations1

VISUAL FOR CHROMATIC ABERRATION 2

Severe purple fringing can be seen at the edges of the horse's forelock, mane, and ear.

VISUAL FOR CHROMATIC ABERRATION 3

On top is corner detail in a photograph taken with a higher quality lens; bottom is a similar photograph taken with a wide angle lens showing visible chromatic aberration (especially at the dark edges on the right).

 

VISUAL 4 A cross made by two black match stick mounted on a cork.

Methods of elimination of chromatic aberration • Achromatic Doublet A combination of convex lens made up of by crown glass and concave lens made up of by flint glass.• Arranging two converging lenses coaxially Two convex lenses made up of by same material arranged coaxially at a distance of d = f1+f2 2

ACHROMATIC DOUBLET• For an achromatic doublet,

visible wavelengths have approximately the same focal length.

• Diffractive optical element with complementary dispersion properties to that of glass can be used to correct for color aberration.

USING TWO CONVEX LENSES If the distance

between the lenses is

d = f1+f2

2

MONOCHROMATIC ABERRATIONS

The deviations in the actual size, shape and position in the image of an object formed by a single lens, when the object is illuminated by single wavelength light.

TYPES OF MONO CHROMATIC ABERRATION

Spherical Aberrations. Astigmatism. Coma. Distortion. Curvature.

SPHERICAL ABERRATIONDef. : The failure or inability of the lens to

form a point image of an axial point object.

TYPES :

Longitudinal : the formation of image in different positions along the axis

Lateral : the formation of image in different sizes perpendicular to the axis.

VISUAL OF LONGITUDINAL SPHERICAL ABERRATION

Side view and chromatic Airy disc of a bright star at image plan. An asymmetry variation of the Airy disk occurs around the paraxial focal plane, displaying spherical aberrations

METHODS OF ELIMINATION OF SPHERICAL ABERRATION

By means of stops. By using two suitable lenses in

contact. By using crossed lens. By using two plano – convex lenses

separated by a distance.

ASTIGMATISM When a point object is

situated far of the axis of a lens, the image formed by the lens is not in a perfect focus.

It consists two mutually perpendicular lines separated by finite distance.

Side view and Airy disc of a bright star coming 25° off axis showing astigmatism; the tangential and sagittal line image do not coincide in the area of less conSide view and Airy disc of a bright star coming 25° off axis showing astigmatism; the tangential and sagittal line image do not coincide in the area of less confusion and in this case display a cross shape.

fusion and in this case display a cross shape

VISUAL OF ASTIGMATISM

Astigmatism as evidenced by the blurring of white dots.

Spoked wheel

.Classic example of astigmatism. Left wheel: no astigmatism. In the presence of astigmatism (middle and right wheels) one discriminates between the sagittal and tangential foci.

ELIMINATION OF SPHERICAL ABERRATIONS

By using two convex

Lenses coaxially at a distance

d = f1 – f2

d = f1 – f2

ELIMINATION OF ASTIGMATISM USING ANASTIGMAT

By using a convex and a concave lens of suitable focal lenghs and separated by a distance . Such a combination is called an anastigmat.

COMA, "comet" in latin

Coma occurs because off-axis rays no not quite converge at the focal plane. Coma is positive when off-axis rays focus furthest from the axis, and negative when they are

closest.

spot diagram showing coma aberration. The resulting image takes the shape of a comet.

ELIMINATION OF COMA using stops Abbe condition µ1Y1SinӨ1 = µ2Y2SinӨ2

Using Aplanatic surface

DISTORTION

The variation in the magnifications produced by a lens for different axial distances results in an aberration called distortion.

It is of two types. 1.Pin cushion . 2.Barrel shaped.

ORIGIN FOR DISTORTION

The influence of stop position on distortion. Note that the image size h differs for a constant object size y.

ELIMINATION OF DISTORTION

A stop is placed in between two symmetrical lenses, so that the pin – cushion distortion produced by the first lens is compensated by the barrel – shaped distortion produced by the second lens.

VISUAL FOR DISTORTION 1

Geometric distortion: the photograph does not flatter the person at the left. (18-mm lens on a 24×36 mm slide)

VISUAL FOR DISTORTION 2

curvature The image of an extended

plane object due to a single lens is not flat one but will be a curved surface. The central portion of the image nearer the axis is in focus but outer regions of the image away from the axis are blurred.

CURVATURE OF THE FIELD DUE TO CONVEX LENS

CURVATURE DUE TO CONCAVE LENS

ELIMINATION OF CURVATURE