Optical systems

2012. 6. 26

WikiOptics

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Contents

1. Eyeglasses

2. The magnifying glass

3. Eyepieces

4. The compound microscope

5. The telescope

6. The Camera

• Source

1) Optics

Hecht, Eugene, 1989, Addison-Wesley Publishing Company, Inc.

2) Wikipedia

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1. Eyeglasses

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Dioptric power

• It is customary and quite convenient in physiological optics to speak about the dioptric power, D, of a lens, which is simply the reciprocal of the focal length.

• When f is in meters, the unit of power is the inverse meter, or diopter, symbolized by D:1m-1=1D.

• For example, if a converging lens has a focal length of +1m, its power is +1D; with a focal length of -2m( a diverging lens), D=-1/2D

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Dioptric power

• We can imagine a double convex lens as being composed of two planar-convex lenses in intimate contact, back to back. The power of each of these:; for the first planar lens(R2=∞),

and for the second,

• These expressions may be equally well defined as giving the powers of the respective surfaces of the initial double convex lens. In other words, the power of any thin lens is equal to the sum of the powers of its surfaces.

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Nearsightedness-Negative lenses

• Myopia is the condition in which parallel rays are brought to focus in front of the retina

• Images of distant objects fall in front of the retina, the far point is closer in than infinity, and all points beyond it will appear blurred. This is why myopia is often called nearsightedness-an eye with this defect sees nearby objects clearly.

• In point of fact, the power of the lens-eye combination is most often made to equal that of the unaided eye. If you are wearing glasses to correct myopia, take them off; the world gets blurry, but it doesn’t change size.

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Nearsightedness-Negative lenses

• What is the equivalent power of a spectacle lens at some distance d from the eye(i.e., equivalent to that of a contact lens with a focal length fc that equals the far point distance)

• Given that the focal length of the correction lens fl and the focal length of the eye is fe

This is the distance from the eye-lens to the retina.

• The equivalent contact lens combined with the eye-lens has a focal length

where f=b.f.l.

independent of the eye itself.

• A spectacle lens of power Dl a distance d from the eye-lens has an effective power the same as that of a contact lens of power Dc.

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Farsightedness-Positive lenses

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• Hyperopia is the defect that causes the second focal point of the unaccommodated eye to lie behind the retina.

• The hyperopic eye can and must accommodate to see distant objects distinctly, but it will be at its limit to do so for a near point, which is much farther away that it would be normally(this we take as 25cm).

• A converging corrective lens with positive power will effectively move a close object out beyond the near point where eye has adequate accuity.

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2. Magnifying glass

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The magnifying glass

• A single positive lens can be used, in effect to add refractive power to the eye, so that the object can be brought still closer and yet be in focus. The lens so used is referred to variously as a magnifying glass, a simple magnifier, or a simple microscope. In any event, its function is to provide an image of a nearby object that is larger than the image seen by the unaided eye.

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The magnifying glass

• The magnifying power, MP, or equivalent, the angular magnification, MA, of a visual instrument is defined as the ratio of the size of the retinal image as seen through the instrument over the size of the retinal image as seen by the unaided eye at normal viewing distance.

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The magnifying glass

• There are three situations of particular interest

(1) When l=f the magnifying power equals doD.

(2) When l is effectively zero,

In that case the largest value of MP corresponds to the smallest value of L, which, if vision is to be clear, must equal do. Thus,

Taking do=0.25m for the standard observer, we have

As L increases, MP decreases, and similarly as l increases, MP decreases. If the eye is very far from the lens, the retinal image will indeed be small.

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The magnifying glass

(3) This last is perhaps the most common situation. Here we position the object at the focal point (so=f), in which case the virtual image is at infinity(L=∞).

for all practical values of l.

Because the rays are parallel, the eye views the scene in a relaxed, unaccommodated configuration, a highly desirable feature.

Notice that MT=-si/so approaches infinity as sof, whereas in marked contrast, MA merely decreases by 1 under the same circumstances.

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DdoL[MP]

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The magnifying glass

• A magnifier with a power of 10D has a focal length (1/D) of 0.1m and a MP equal to 2.5 when L=∞.

• This is conventionally denoted as 2.5X, which means that the retinal image is 2.5 times larger with the object at the focal length of the lens than it would be were the object at the near point of the unaided eye(where the largest clear image is possible).

• The simplest single-lens magnifiers are limited by aberrations to roughly 2X or 3X.

• The figure shows a few more

complicated magnifiers designed

to operate in the range from

roughly 10X to 20X.

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3. Eyepieces

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Eyepieces

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• The eyepiece, or ocular, is a visual optical instrument. Fundamentally a magnifier, it views not an actual object but the intermediate image of that object as formed by a preceding lens system.

• The ocular must provide a virtual image(of the intermediate image), most often located at or near infinity, so than it can be comfortably viewed by a normal, relaxed eye. Furthermore, it must position the center of the exit pupil or eye point at which the observer’s eye is placed at some convenient location, preferably at least 10mm or so from the last surface. As before, ocular magnification is the product doD, or as it is often written, MP=(250mm)/f.

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Eyepieces

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• Huygens eyepiece

- Eye relief is only an uncomfortable 3mm or so.

- Cannot be used as a magnifier.

• Ramsden eyepiece

- Eye relief is about 12mm.

- Reticle can be used.

• Kellner eyepiece

- Represents a definite increase in image quality.

- Eye relief is between that of the previous two devices.

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Eyepieces

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• Orthoscopic eyepiece

- Wide field

- High magnification

- Long eye relief(~20mm)

• Symmetrical(Plössl) eyepiece

- Superior to orthoscopic.

• Erfle eyepiece

- Probably the most common wide-field (roughly ±30°).

- Well corrected for all aberrations

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4. The compound microscope

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The compound microscope

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• The compound microscope goes a step beyond the simple magnifier by providing higher angular magnification ( greater than 30X) of near by objects.

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The compound microscope

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• The magnifying power of the entire system is the product of the transverse linear magnification of the objective, MTo, and the angular magnification of the eyepiece, MAe, that is,

• MT=-xi/f. Most manufactures design their microscopes such that the distance(corresponding to xi) from the second focus of the objective to the first focus of the eyepiece is standardized at 160mm. The distance, known as the tube length, is denoted by L.

• With the final image at infinity and the standard near point taken as 10 inches (254mm),

and the image is inverted(MP < 0). Accordingly, the barrel of an objective with a focal length fo of, say, 32mm will be engraved with the marking 5X (or X5), indicating a power of 5. Combined with a 10X eyepiece(fe=1 inch), the microscope MP would then be 50X.

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The compound microscope

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• The objective itself functions as the aperture stop and entrance pupil. Its image, formed by the eyepiece, is the exit pupil into which the eye is positioned. The field stop, which limits the extent of the largest object that can be viewed, is fabricated as part of the ocular.

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Magnification by Wikipedia

• For a compound microscope the corresponding formula is

where

D is the distance of closest distinct vision (usually 250mm)

Deo is the distance between the back focal plane of the objective and the back focal plane of the eyepiece(called tube length), typically 160mm for a modern instrument

fo is the objective focal length and fe is the eyepiece focal length

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Melles griot

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• Finite-conjugate microscope & Infinite-Conjugate microscope

• Older microscope objectives(before 1980) were designed to form an image at a given distance(the tube length) behind the objective flange.

This distance varied between 160mm and 210mm depending on the manufacturer and the application.

• Modern microscope objectives are

“infinity corrected”. They are optimized to provide collimated light on their image side. A separate decollimating or tube lens then forms image. This design gives microscope manufacturers flexibility to insert lighting and beamsplitters in the collimated space behind the objective.

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5. The telescope

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Refracting telescopes

• Unlike the compound microscope, which it closely resembles, its primary function is to enlarge the retinal image of a distant object.

• The object is at a finite far distance from the objective, so that the real intermediate image is formed just beyond its second focal point. If the eyepiece is to form a virtual magnified final image, the object distance must be less than or equal to the focal length, fe.

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Refracting telescopes

• The angular magnification is

• Furthermore, if Do is the diameter of the objective and Dep is the diameter of its image, the exit pupil, then

Here Dep is actually a negative quantity, since the image is inverted.

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Reflecting telescopes

• The problem in making large lens

– A lens must be transparent and free of internal bubbles

* A front-surfaced mirror obviously need not be so, indeed it need not even be transparent

– A lens can be supported only by its rim and may sag under its own weight

* A mirror can be supported by its rim and back as well

– Chromatic aberration

* Mirrors suffer no chromatic aberration

• For these and other reasons(e.g., their frequency response), reflectors predominate in large telescopes.

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Catadioptric telescopes

• A combination of reflecting (catoptric) and refracting(dioptric) elements is called a catadioptric system. The best known of these, although not the first, is the classic Schmidt Optical system.

• It represents the precursor of a new outlook in the design of large-aperture, extended-field reflecting systems.

• This first system was built in 1930, and in 1949 the famous 48-inch Schmidt telescope of the Palomar Observatory was completed. It is a fast(f/2.5), wide-field device, ideal for surveying the night sky. A single photograph could encompass a region the size of the bowl of the Big Dipper(북두칠성의 사발)-this compared with roughly 400 photographs by the 200-inch reflector to cover the same area.

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6. The camera

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Camera obscura

• The prototype of the modern photographic camera was a device known as the camera obscura, the earliest form of which was simply a dark room with a small hole in one wall. Light entering the hole cast an inverted image of the sunlit outside scene on an inside screen.

• camera obscura (Latin; camera for "vaulted chamber/room", obscura for "dark", together "darkened chamber/room)

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18th century artist using a camera obscura to outline his subject.

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Pinhole camera

• The lensless pinhole camera is by far the least complicated device.

• It can form a well-defined, practically undistorted image of objects across an extremely wide angular field (due to great depth of focus) and over a large range of distances(great depth of field)

• In most practical situations, the pinhole camera’s one overriding drawback is that it is insufferably slow(roughly f/500).

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Light rays from an object pass through a small hole to an inverted image.

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SLR

• SRL(single lens reflex)’s structure

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Cross-section view of SLR system: 1: Front-mount lens (four-element Tessar design) 2: Reflex mirror at 45-degree angle 3: Focal plane shutter 4: Film or sensor 5:Focusing screen 6: Condenser lens 7: Optical glass pentaprism (or pentamirror) 8: Eyepiece (can have diopter correction ability)