Optical Instruments • Camera – Image size, brightness, exposure time •The eye – Parts and basic functions – Visual acuity, why we need optical instruments • Microscope – Simple magnifier, compound microscope, terminology • Telescopes – Newtonian, Galilean, terrestrial – Binoculars, field of view – Laser beam expanders – Image relaying

March 03 LASERS 51 Simple camera Aperture stop Field stop

Film

Object light baffle Image

Focal plane

Landscape Lens • Single meniscus lens (known as landscape lens) • A large field of view is desired (since landscapes are large) – Some attempt at reducing astigmatism, coma and field curvature is made by adjusting the shape of the lens and the position of the stop • Spherical aberration is controlled by reducing aperture size – Large f/# (slow, landscapes don’t move)

March 03 LASERS 51 Image size vs focal length ch f ief ray

Both lenses ch have same ief f object, at a ray large distance

• Image size is proportional to the lens focal length – Focal length is distance from principal plane to focal point f

Telephoto lens principal plane March 03 LASERS 51 Light gathering power in a camera rays not getting Aperture stop to film plane

Aperture stop diameter Small f/#, brighter image f=focal length D=aperture stop focal length diameter rays not getting Aperture stop to film plane f/# = f/D

Aperture stop diameter Large f/#, dimmer image

• Rays carry energy focal length – More rays getting to film plane gives brighter image • Image size and location are not affected!!!! March 03 LASERS 51 Exposure of film depends on total light energy incident on film • Larger aperture Aperture stop stop – More rays get to image D – Image brighter shutter open – Less time needed shutter closed 0 10 for exposure of time (milliseconds) focal length film

Aperture stop • Smaller aperture stop – Image not as bright

shutter open D – Longer exposure

shutter closed time needed 0 40 time (milliseconds) focal length

March 03 LASERS 51 F-stops and exposure time • f-stop refers to the aperture stop NOT FIELD STOP – Called f-stop because it is connected with the f/number • Number of rays collected is proportional to area of aperture, 2 i.e. D 2  1  D2   = – Brightness (irradiance) proportional to   2  f /#  f – Increasing f/# by 2 decreases image irradiance by 4 • Exposure=total amount of light collected by the detector

(film, CCD, etc.) 2during time that the shutter is open  1  – Exposure ∝   • E.T . , E.T.=exposure time (shutter open time)  f /#  – For larger f/#, the exposure time must be longer to get the same total light on the detector, thus optical system is slower

March 03 LASERS 51 Standard F-stops • Standard f/stops in cameras change image irradiance by 2 – Diameter of aperture changes by √2 (e.g. 5.6, 4.0, 2.8) • Smallest possible f/# corresponds to the aperture stop fully open

Focal length Dmax= 50mm/1.7=29.4mm Smallest f/#

Aperture settings

March 03 LASERS 51 Charge-coupled devices (CCD) • Each square represents a separate detector – Light creates electrons in each box as long as shutter is open – Electrons are trapped in the box until readout begins • Electronic signals during readout shift electrons from one box to another – One row is shifted first – First row then shifted to readout row. Columns in readout row are then shifted to output – Continue until all rows readout

March 03 LASERS 51 A complex optical system-the eye • Several refractive surfaces – Cornea largest power –Lens • gradient index • aspheric surfaces • variable power • Aperture stop at iris is variable from ~3-7 mm • Scattered light limited by pigment epithelium • Detector has two different types of elements – cones for color, rods for low light levels – fovea, high concentration of cones, no rods, most acute vision March 03 LASERS 51 Optical properties of a “standard” eye

n=1.33

n=1.33

n=1.38-1.41

• All dimensions in millimeters • Eye shown relaxed (focused at infinity) • Nodal points and principal planes differ • Primary and secondary focal lengths differ March 03 LASERS 51 Subtend – Latin 101 sub[tend 7s!b tend$8 vt. 5L subtendere < sub-, under + tendere, to stretch: see TEND26 1 to extend under or be opposite to in position !each side of a triangle subtends the opposite angle"

Sub – submarine, subordinate, subliminal, sublease, sublunar Tend – as in to have a tendency to extend, tendon, contend, tent Line subtends angle α at point P

α d=length of line P L=distance to point P Note, for α in radians α=d/L, approximately

March 03 LASERS 51 Visual acuity (how small an object can be seen)

s’ y’, image height Θ, angle y’=Θs’ subtended by object at eye Image on retina • Spacing between cones (detectors) in fovea ≈ 2.5µm – For a smaller image, details in the image are not observed • You may still be able to tell that something is there – Minimum subtended angle = 2.5µm/17.1mm=.15mr=0.5’ • 0.5’ means 0.5 minutes of arc (60 minutes = 1 degree)

To see more detail, the image must be made larger by bringing the object closer to the eye. This increases the subtended angle.

March 03 LASERS 51 Acuity in real eyes • Typical eyes have only slightly worse resolution – This means that the design of the lens system is very well matched to the detector • If the cones were closer together, you wouldn’t get better resolution because the aberrations of the lens would blur the image • If the lens were better corrected, it wouldn’t help because cone spacing limits resolution • Diffraction also plays a role in resolution – If pupil size = 4 mm, f/# ≈ 4.8 (n’=1.33) diffraction limited spot size = ~ 5µm, resolution ~ 1’ – This corresponds to 1.5 ft at a distance of 1 mile, or 0.07mm at 250mm

March 03 LASERS 51 Near point • Bringing object closer improves resolution – Lens of the eye changes focal length so image is on the retina – Lens can only bend a limited amount • Once lens is bent to minimum focal length, bringing object closer doesn’t improve resolution because the eye can’t focus on it • Near point is closest point that an object can be imaged – Lens of eye is made as strong as possible (largest power, shortest focal length) – For a standard eye the near point is at 25 cm = 250 mm – Smallest feature that can be resolved is 0.3mr*250mm=75µm – If the lens cannot be bent enough to bring the near point in to 250 mm, the eye is presbyopic (old), lens is too stiff for cilliary muscles to bend it

March 03 LASERS 51 Far point

• Far point is farthest point that an object can be imaged – Lens of eye is made as weak as possible (smallest power) • cilliary muscles relaxed, most comfortable viewing – The far point for a standard eye is infinity • Defects of the eye’s focusing ability at long distances – If the fully relaxed eye images an object at a distance of less than infinity the eye is myopic (near sighted) – If the eye is not fully relaxed when viewing an object at infinity the eye is hypermetropic (far sighted)

March 03 LASERS 51 Spectacle lenses Contact lenses work the same way. They are slightly less powerful (thin lenses in contact), and also can be thin since they are small in diameter (sag formula). Note f only depends on radii.

• Positive lens (reading glasses) also used to correct presbyopia, the inability of the lens to accommodate • Cylindrical lenses used to correct astigmatism due to a nonsymmetric cornea • Excimer laser can be used to ablate some of the cornea and therefore change its shape, but can’t make lens more flexible March 03 LASERS 51 Visual optical instruments • Very small objects cannot be resolved by the naked eye – Best resolution when object placed at near point – “Resolved” means making out details of the object, the presence of a very small object can be detected if it emits enough light • Very distant objects cannot be resolved by the naked eye – Why? The angle subtended by a distant object can be small even if the object is very large, e.g. a star – The same comment about resolution applies here. Obviously we can see stars, but we cannot make out any details about them as we can for example make out details on the moon’s surface. – Sometimes distant objects cannot be seen because the eye’s pupil does not collect enough light • Visual optical intsruments solve one or the other of these problems

March 03 LASERS 51 Simple microscope (magnifier) • To examine small objects (<75µm) a simple positive lens can be used – allows the object to be brought closer to the eye – Image is produced at a point comfortable for viewing, far point – Shown as a single lens here, but may be multi-element Image at infinity

h

f Without magnifier, Angular object at near point With magnifier magnification h h 250mm angular size = angular size = 250mm f f

March 03 LASERS 51 Other ways to use a magnifier • Angular size h' subtended by image is h/s h – Since s

Important: when a magnifier is specified as 10x, this refers to the case of the image at infinity March 03 LASERS 51 Angular magnification demystified (I hope) Unaided eye Eye has minimum focal length h h h′ = s′tan(α) = imageh' on 25cm α retina near point, 25 cm

Using magnifier s' Eye focused at f infinity (relaxed) α' h h h2′ = s′ tan(α′) = f α' h2'

paralle l h′ tan(α′) 25cm 2 = = • Image on retina made larger by lens h′ tan(α) f – Eye lens changes to image on retina • Increase in size is linear magnification

March 03 LASERS 51 More on angular magnification

h s f s ' (negative) α’ determined by Definition of angular α determined by chief ray magnification near point tan(α′) h β = h tan(α′) = tan(α) = s tan(α) 25cm • Angular magnification can be larger than 25cm/f – Image will no longer be at infinity (far point) • Can also be derived from image size on retina

March 03 LASERS 51 Compound microscope, for smaller objects Objective lens Eyepiece (ocular)

real, magnified image from objective • Objective lens forms a real, magnified image

– magnification=Mobjective • Eyelens (also ocular or eyepiece) used to view the image – Works just like simple magnifier discussed earlier

– Angular magnification=Meyepiece • Total magnification=Mobjective*Meyepiece • The eyepiece can replaced with a camera or CCD • A reticle can be inserted at the location of the real image – Used to measure the object for example

March– 03 Will appear to be at the same plane as the object LASERS 51 Microscope terminology focal point

tube length

working distance real focal point image • Tube length = 160 mm for most standard microscopes • From Newtonian imaging equation (easiest way) – Magnification=-160mm/f – This is (approximately) the number stamped on the side of a microscope objective • Eyepiece magnification stamped on side is 25/f – Be careful of units, this formula is in cm – You can use this eyepiece for larger magnification also (see previous discussion on magnifiers and angular magnification) March 03 LASERS 51 Infinity-corrected microscopes Infinity-corrected objective lens tube lens Eyepiece

• Light from objective is collimated • More flexibility in layout of microscope • Gives collimated beam for placing filters, polarizers, etc. • Infinity-corrected objectives and ordinary objectives cannot be interchanged without sacrificing image quality

March 03 LASERS 51 Illumination in microscopes Infinity-corrected light objective lens tube lens Eyepiece source

condenser lens • Usually the object for a microscope does not emit light itself, it must be illuminated by a separate light source • There is more than one way of doing this depending on the particular application • The quality of the image you obtain depends critically on proper adjustment of the illumination • For an object which is not transparent, reflected light is used, illumination comes from other side using beam splitters

March 03 LASERS 51 Telescope-introduction

• Some objects (e.g. moon, planets, distant objects on earth) cannot be brought up close for examination • If these objects subtend too small an angle to be resolved by the eye, we need to increase their angular size in order to examine them • A pair of lenses arranged so that the secondary focal point of one lens coincides with the primary focal length of the other can provide the needed angular magnification – This can be called a confocal system

March 03 LASERS 51 Telescope-basic principles Entrance pupil common Exit Θ1 at objective focal point pupil Objective Eyelens

Axial ray Chief ray Θ2 from distant object f_2 Field stop f_1 at eyelens • Angular magnification is Θ2/Θ1=f1/f2 • Axial ray from infinite object emerges parallel to axis – called afocal system (focal points at infinity)

– axial ray height ratio = f2/f1 • Telescope with two positive lenses called Newtonian (or Keplerian) – image inverted – Objective is aperture stop and therefore entrance pupil – exit pupil behind eyelens, distance to exit pupil called eye relief – field stop at eyelens March 03 LASERS 51 Field of view of a telescope HFOV Exit Objective pupil Eyelens De

Chief ray f_2 Field stop f_1 at eyelens

HFOV=half field of view 1 D HFOV = 2 e (in radians) f1 + f2 180 D field of view = × e (in degrees) π f1 + f2 • Always make sure you know whether you are talking about full or half angle, radians or degrees • A field lens can be used to increase fov

March 03 LASERS 51 Terrestrial telescope Field stop Entrance pupil Chief ray

Axial ray Objective Erector Eyelens A simple terestrial telescope • The Newtonian telescope produces an inverted image – Not much of a problem for a star, but a major annoyance if looking at ships at sea • The erector lens is just a 1:1 imaging lens – As a result a terrestrial telescope is longer than a Newtonian telescope with the same focal lengths

March 03 LASERS 51 Binoculars • Binoculars are essentially just a pair of terrestrial telescopes – Normally a pair of Porro prisms is used to invert the image rather than an erector lens. This allows the two objectives to be placed farther apart • Binoculars are usually specified by their angular magnification and the size of their objective – (6x30) means 6x angular magnification and 30 mm diameter objectives – Exit pupil, field of view, eye relief found just as for the telescope

March 03 LASERS 51 Gallilean telescope Entrance pupil at objective Exit common pupil focal point Objective Eyelens

Axial ray Chief ray from distant object f_2 f_1 Field stop at eyelens • Telescope shorter for same magnification • Image is erect • Exit pupil not accessible to eye

March 03 LASERS 51 Reflecting telescope • In principle, the reflecting telescope is just like the refracting telescope except that the objective lens is replaced by a concave mirror • Important differences – Much larger objectives can be made •Lighter • Easier to support • Less material constraints – No chromatic aberration – Different shapes can be made to compensate other aberrations fairly easily (for example a parabola)

March 03 LASERS 51 Why a 10 meter objective?

• An earthbound telescope does not provide better resolution of objects after it gets over about 30 cm in diameter – Atmospheric turbulence is the limitation – Can be overcome by adaptive optics • Nevertheless, the larger the objective, the more light is collected (smaller f/#) allowing fainter objects to be observed

March 03 LASERS 51 Laser beam expander f2 Lens 1

f1 Lens 2 • Similar to telescope – Magnification=f2/f1 (can be smaller or larger than one!) – Focal points of the lenses coincide (collimated in/collimated out) – Not only increases size, but reduces beam divergence • Important practical points – Flatter sides of lens face towards inside to minimize aberrations • Plano-convex often adequate, but best-form or even multielement needed sometimes – Internal waist can be used for spatial filter, but can cause air breakdown or other problems for high-power lasers

March 03 LASERS 51 Galilean beam expander Lens 2 Lens 1

f1 f2 • As in Newtonian form, focal points coincide • Flatter sides also towards center – Rule of thumb, if each surface does about the same amount of bending aberrations will be minimized • Note that there is no internal focus and for the same magnification, this telescope is shorter

March 03 LASERS 51 Image-relay systems

f1 f1 f2 f2

• Again similar to telescope, focal points coincide • Flat sides of lenses towards inside • Can be combined with beam expander/spatial filter for laser beams with image information on them • No Galilean form (at least not with real object)

March 03 LASERS 51 Image relay in high-power laser systems • High-power laser systems use beam expanders to increase the beam size as the beam travels from the smaller amplifiers to the larger ones • All high-power laser amplifier chains that I am aware of use Keplerian rather than Galilean beam expanders – In most cases, a small aperture (pinhole) is placed at the focus • Not only functions as a spatial filter, but also blocks dangerous back reflections – Imaging from one amplifier to the next is crucial to getting high power without damaging components • Errors in beam due to imperfections in amplifiers, or small damage spots, etc. lead to larger variations of beam intensity out of the image plane – The Keplerian expanders require evacuated tubes, but this is a small price to pay for not blowing up expensive laser glass March 03 LASERS 51 Some other important optical systems • Projector system • Microscope illuminators • Energy concentrators (e.g. focus light on a detector, or a missle) • Lighting systems • Anamorphic systems (cylindrical optics) • Catadioptric systems (reflection and refraction) • Measuring systems • Adaptive optical systems • Numerous specialize applications

March 03 LASERS 51