OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-1 Section 3 Imaging With A Thin Lens OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-2 z z ed set of rays entering the optical system. t the rays become more parallel. t the rays become rays become parallel or collimated. An image at infinity collimated An is also represented by rays. When the object goes to infinity, the object goes When Consider the rays from a finite Consider object located on the axis. more distan the object becomes When An object at infinity produces a set of collimat object at infinity An produces Object at Infinity OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-3 z z z infinity. Without a at negative infinity or an image at positive intersect at a point object at infinity or an image at infinity. we are discussing positive or negative infinity. we z rve as an object at negative infinity: y to tell an object from image: One way to think of this is that parallel lines to think of way One Parallel rays are used to represent either an Parallel rays are used lens, these rays could represent either an object lens, these rays could lens, it is eas infinity. With a But an image at positive infinity can se matter if not it does Infinity is infinity and Parallel Rays OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-4 z z the optical system, but at an angle with the optical system, but at an ed, but the approximation is incredibly good! –rays from that at a great distance. The just axis and the image will be on the optical axis: the image will be on axis and age is formed off the optical axis. off the age is formed An on-axis object is aligned with the optical off-axis object, collimated light still For an enters im respect to the optical axis. The In practice, no object is ever really at infinity In practice, no distant object point are “approximately” collimat On Axis and Off – Object at Infinity OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-5 z of the lens. F' rear focal length rear of the lens F'. st always used in air (n = n' 1.0) and is ns*. A thin lens is an optical element with A ns*. R to describe both of these idealized elements. f so have zero thickness, may aberrations. axial lenses” which are perfect first-order axial lenses” which f that cross at the rear focal point. R f Rear Focal Point -rays rays parallel All to the axis produce -distance from the lens to rear focal point is The Many optical systems are first as a thin le modeled zero thickness that has refracting power. It is almo zero thickness that has refracting power. its characterized by focal length f. object at infinity An is imaged to the * This discussion should actually refer to “par should This discussion * lenses of zero thickness. Thin lenses, which al lenses of zero thickness. the term “thin lens” is commonly used However, Imaging with a Thin Lens in Air OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-6 z of the lens front focal length f emerge from the lens parallel to the axis. F f F f of the lens F is imaged to infinity. F Front Focal Point - rays crossing at the front focal point All -distance from the lens to front focal point is The An object at the An which equals minus the focal length. Thin Lens –Thin Lens Focal Point Front OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-7 z ' h Image Conjugate z' ned as the ratio of image height to ft of the lens has a negative object distance. ' h h its image) is related by their magnification. its image) is related by has a unique, associated magnification. m que pair que of conjugate planes. z') or object and image distances. z') or object and at the magnification is also negative. f = Focal Length f = Focal z h Object Because of sign conventions, an object to the le of sign conventions, Because The magnification of this object and image is defi magnification of this object and The object height: In this figure, h' is negative so th A pair of conjugate planes (the object and pair of conjugate A - given magnification defines a uni A -object position z, there is a single image location z'. every For -object position (or image position) Each Thin Lens - Conjugates An object and its image are conjugate, and the respective distances from lens are and its image are conjugate, object and An called conjugate distances (z and OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-8 F R ff ff z h' ' z F' the image position, magnification, and R f m the properties of focal points. f intersection of these two rays. h F f intersection of two rays. z F h The two rays that are normally used are: -the rear focal point. through ray parallel to the optical axis emerges A - parallel to the optical axis. the front focal point emerges ray through A - point A is defined by the - two rays intersecting Construct at the object point. -rays. conjugate the two Determine -at the image point is found The the focal length can be determined fro The relationships between the object position, relationships The between Thin Lens – Relationships Imaging OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-9 z z h F F R R f f ft of the front focal point F F F f f F F h h Positive Lens– object to the le Real Locating an Image with the Focal Points –Locating an 1 Example OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-10 z z F F ossing. An enlarged, erect virtual An enlarged, image is ossing. R R f f ght of the front focal point F the front focal point ght of F F f f h h F F h produced. The image is in space. The produced. The two image rays diverge and have a virtual cr The two image rays diverge Positive Lens– object to the ri Real Locating an Image with the Focal Points –Locating an 2 Example OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-11 0 0 '
F R ff ff R ' f f R zf f m ' z 1 '' R ' zz f tan h h R z 11 RR f m hh '' ff zz m h' ' 1 m z F' ' 1 F z f F R stances for a particular magnification. F f f tan h' f F 1 zz ' FF h 1 ff hzf h 11 hh F f z fm z 1 m mf f z F h Thin Lens –Thin Lens Relationships - Imaging Derivation Similar triangles: These equations give the conjugate di OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-12 z ' h ' z z m z' F' ate thickness is zero for an ideal thin lens. very thin plane parallel plate. The ray is not ray The parallel plate. thin plane very z and z' z and (eliminating f), take the ratio of R f from the object point to image must h' f m h F f 1 f z F 1 mf 1 m 1 '1 zm zm h deviated, and it displacement is zero since the pl deviated, and The center of the lens can be considered to be a to be center of the lens can be considered The the last two equations: ray drawn implies that a This last equation the center of lens. pass through To determine the magnification as a function of Thin Lens - Magnification OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-13 ured from the lens (and therefore usually from what is usually stated due to sign from what is usually stated due image conjugate distances directly image conjugate with the f z m ' 1 zz 1 ' '' ' f f z zz f 111 111 zz This form of the imaging equation differs This form of the imaging equation differs conventions. We use an object distance meas We conventions. negative.) focal length (eliminate the magnification). for z'Return to the equation in terms of m: One final result is to relate the object and final result is to relate the One Thin Lens – Equation Imaging OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-14 ' ' 11 1 oi f 111 zzf zo zi z z ' ' h h Image Image z' i to make easy problems harder, but to make easy problems harder, There is inconsistency in the defined object and image distances There is inconsistency in the defined object and z o h h Object Object The use of sign conventions may appear their use will make hard problems possible. Traditional representation: Sign convention representation: Sign convention Impact of Sign Conventions –Impact of Sign Conventions Equation Imaging OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-15 RF 0 0 ff 0 F R f f f f Positive Lens: z Object Position 4f 2f z' Image Position 6f 2f 4f -4f -6f -2f 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 Positive Lens -2f -4f -5 -4 -3 -2 -1 0 1 2 3 4 5 Thin Lens – Positive Lens – Conjugates OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-16 z h e Rear Focal Point F' of the lens. the Front Focal Point F of lens. F Real Image Space A real object and a real image are shown. real object and A Virtual Object Space Virtual with real and virtual segments to
F Real Object Space Virtual Image Space Virtual h Object Space – the Object and Contains Image Space – the Image and th Contains The thin lens creates two optical spaces: The Both optical spaces extend from Optical Spaces OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-17 z rtual segments. The ray must meet space. Within both optical spaces, a ray is virtual image is to the left of the lens. virtual object is to the right of lens. with real and vi with real and to A real image is to the right of lens; a A A real object is to the left of the lens; a A straight and extends from straight extends and Rays can be traced from object space to image and be continuous at the lens. Optical Spaces and Rays Optical Spaces and OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-18 z F' formed either to the right or left of side of the front focal point F. lens (z'be viewed 0). These images can > F F ff F or This image cannot currently be displayed. always goes from left always to right. zf zf The real object must be located out The Depending on the object position, image may be on Depending the thin lens. Remember, light Real images are formed to the right of thin placing a screen at the image plane. by To obtain a real image with a positive lens: Thin Lens – Object and Real Image Real OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-19 z F' F front focal point F and the lens. front focal point F and s to be coming from the virtual s image point. thin lens (z'images cannot be 0). These < 0 f or 0 fz0 fz z F ff F Object Image The real object is located between real object is located The The image appears to be behind the lens. This is the situation that occurs with a magnifying glass. appear from the lens and light The diverges directly viewed on a screen. To obtain a virtual image with a positive lens: Virtual images are formed to the left of the Thin Lens – Object and Virtual Real Image OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-20 z z Image Object Image F' z0 z0 an image is projected into the lens by an ts the rays before they come to focus. 0 F z System System Imaging Imaging The imaging equations hold for any of these situations. Thin Lens – Virtual Object another imaging system. The lens intercep another imaging system. a positive lens, real image will be produced. With Virtual objects are also possible and occur when objects are also possible and occur Virtual This image serves as the virtual object for the inserted lens. OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-21 z z h h F F e virtual object –parallel to the axis and one h R R f f F F f f F F one through F. These rays refract to produce the real, minimized image. one through F. Two object rays are constructed that define th Two Positive Lens– object to the right of lens Virtual Locating an Image with the Focal Points –Locating an 3 Example OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-22 ' z z z m z z Real Object-Real Image z z 3f F' F' F' F' F' 2f 1.5f f -f -1.5f F F F F F -2f -3f Imaging with a Positive Lens OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-23 ' ' z z z z m m z z Virtual Object-Real Image Object-Real Virtual Real Object-Virtual Image Real Object-Virtual F' F' 2f .67f -.75f F F -3f Imaging with a Positive Lens OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-24 z z F' F' at the top of the lens is bent by the same at the top of lens is bent by position. There is a fixed relationship object ray will change and the ray pair will and object ray will change side the rear focal point and the image must side the rear focal point and rsection point on the lens with a fixed bending. sualizing the image position for a given object infinity. This defines the ray bending. the front focal point of lens: Ray Bending amount independent of the input ray or object the image ray. the object ray and between First object at consider the rays for an In the ray drawings, note that the ray incident In the ray drawings, This relationship can be a great aid in vi This relationship can position. As the object position changes, the the object position changes, As position. to pivot or rotate the ray inte appear about For a finite conjugate object outside It is easy to see that the image position is out that the image to see It is easy be real. OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-25 z z z F' between the lens and the rear focal point. the lens and between a certain height on a lens is not a constant in ray slope or the tangents of angles. e lens must produce a virtual image. There e lens must produce point, the image must be at infinity: F F A virtual object must produce a real image located a virtual object must produce A The fixed ray bending forces the image to fall short of the rear focal point. fixed ray bending The As will be shown later, at the constant ray bending later, As will be shown change in ray angle, but rather a constant change change When the object is at front focal When An object between the front focal point and th the front focal point and object between An is not enough ray bending to produce a real image. to produce ray bending is not enough Ray Bending – Continued OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 0 0 3-26 0 0 z z z z RF 0 0 ff 0 F R f f f f Real Object Real Image Object Virtual Image Virtual Positive Lens: z Object Position 4f z' > 0 Real Image 2f z' Image Position 6f 2f 4f -4f -6f -2f 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 Positive Lens -2f z < 0 -4f Real Object -5 -4 -3 -2 -1 0 1 2 3 4 5 Thin Lens – Positive Lens – and Virtual Real Images OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp + 3-27 0 ∞ - z en reappear as a virtual image coming in from correspond to either a real image at positive to either a real image correspond point, there is an ambiguity as to the image oves through the front focal point, image will oves through en the object is at front focal point. en F - Infinity Positive - Infinity Negative “The real projective line” location: these could and Collimated rays are produced infinity or a virtual image at negative infinity. Positive infinity and negative infinity cannot be distinguished. Note that when the object is at front focal that when Note Object at the Front Focal Point There is a mathematical concept that space “wraps” around at infinity: Applying this to imaging: As a real object m a real object As this to imaging: Applying th as a real image to positive infinity and move The transition point is wh negative infinity. OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-28 with a focal length of 100 mm. Where is the with a focal length of 100 [ ] a. 125 mm to the left of the lens [ ] a. 125 mm to the right of lens [ ] b. 125 mm to the right of lens [ ] c. 83.3 mm to the left of the lens [ ] d. 83.3 An object is 500 mm to the left object is 500 of a thin lens An image located? Mini Quiz OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-29 z 125 zmm Image z' f with a focal length of 100 mm. Where is the mm. with a focal length of 100 f = 100 m ' 111 zz z mm 500 100 Object f zmm [ ] a. 125 mm to the left of the lens [ ] a. 125 mm to the right of lens [X] b. 125 mm to the right of lens [ ] c. 83.3 mm to the left of the lens [ ] d. 83.3 An object is 500 mm to the left object is 500 of a thin lens An image located? Mini Quiz –Mini Quiz Solution OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-30 z RF 0 F 0 ff 0 R F f f f f Negative Lens: F f f R f z F' nd will diverge light. The front and rear front and light. The will diverge nd F F f f R f F' focal points are reversed and are virtual. focal points are reversed and A negative lens has a focal length a Thin Lens – Lens Negative The imaging equations also hold for a negative lens, and a virtual image is produced for a real object (z < 0). OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-31 RF 0 0 ff 0 R F f f f f Negative Lens: z Object Position 4|f| 2|f| 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 6|f| 2|f| 4|f| -4|f| -6|f| -2|f| Negative Lens z' Image Position -2|f| -4|f| -5 -4 -3 -2 -1 0 1 2 3 4 5 Thin Lens – Lens – Negative Conjugates OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-32 z ' z z m F -2f 0 Real Object-Virtual Image Real Object-Virtual -.67f f Virtual Object-Virtual Image Object-Virtual Virtual z z F' F F .75f -2f F' 3f F' 2f Virtual Object-Real Image Object-Real Virtual Imaging with a Negative Lens OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-33 z z ocated between the rear focal ocated between is by case, the object ray is bent outward infinity. This defines the ray bending. infinity. This defines the ay will change and the ray pair will appear to pair will appear the ray and will change ay so be used with negative lenses to visualize the tion point on the lens with a fixed bending. ect, a virtual image must be l F' F' Ray Bending – Lens Negative point and the lens: point and For a real finite obj conjugate As the object position changes, the object r As the object position changes, pivot or rotate about the ray intersec image position for a given object location. In th image position for a given the lens: As before, consider the rays for an object at The fixed ray bending concept can al OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-34 is not a constant change z z s of the ray angles. z nt will produce a real image: a nt will produce point will produce a virtual image point will produce tain height on a lens a tain height on produces an image at produces infinity: F F F ray slope or the tangent lens and the front focal poi lens and F' or outside the front focal focal point of the lens side the rear focal point: in ray angle, but rather a constant change in in ray angle, but rather a constant change As noted earlier, the constant ray bending at a cer As noted earlier, A virtual object between the virtual object between A A virtual object to the right A located to the left or out Ray Bending – Lens – Negative Continued A virtual A object at the front OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 0 0 0 0 3-35 z z z z RF 0 0 ff 0 R F f f f f Negative Lens: Real Object Real Image Object Virtual Image Virtual z Object Position 4|f| z' > 0 Real Image 2|f| 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 6|f | 2|f| 4|f| -4|f| -6|f| -2|f| Negative Lens z' Image Position -2|f| z < 0 Real Object -4|f| -5 -4 -3 -2 -1 0 1 2 3 4 5 Thin Lens – Lens – Negative and Virtual Real Images OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-36 z z crossing. A minified, erect virtual minified, erect A crossing. of the Focal Points. The Front Focal The of the Focal Points. lens. Similarly, the Rear Focal Point F'lens. Similarly, is F F f f R R h f f space of the lens. The same image formation rules apply. space of the lens. FF FF h h Negative System – Real object – the Note locations of the in the object space Point F is virtual and also virtual in the image and The two image space rays diverge and have a virtual The two image space rays diverge image is produced. The image is in image space. image is in The image is produced. Locating an Image with the Focal Points –Locating an 4 Example OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-37 z 2 f h Image 2 222 z 111 zz 2 f he first lens serves as the object for 2 ough a series of lenses by imaging through z 2 12 12 zz zz 12 h t 21 1 zzt tz z of the individual magnifications: h 1 Intermediate the elements in system. Image/Object z 12 1 2 1 f mmm m m 1 z 111 111 zzf 1 h Object The process is repeated for all of The net magnification is the product The the lenses one at a time. The image produced by t by image produced at a time. The the lenses one second lens, etc. Cascaded imaging is the process of imaging thr Cascaded Cascaded Imaging OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-38 0 z 0 2 z 2 1 z h 1 h Intermediate Image/Object f stance for the second lens: 2 z 2 222 h 111 zz Image 2 z 2 f produces a virtual produces image or . that for the object di 12 12 1 zz zz z 12 21 zzt tz z t 12 1 2 ate image/object will be virtual: ate image/object will be mmm m m 1 f 1 111 111 z zzf 1 h Object In most cases, the intermedi All of the same relationships including hold, relationships The are also valid if the first lens Cascaded Imaging OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-39 by the object distance. zf zz zz zf rear focal point. = 1): ' focal length divided more than a few times the magnitude of is approximately equal to the rear focal Lz Lz ed just outside the : : zfzfLzzzfm zfzfLzzfzm There are similar approximations for distant images: The magnification can be approximated by the L is the object-image distance. L For a distant object, the image is locat the system focal length, image distance z' (n = n positive thin lens in air is assumed length. A When the magnitude of object distance z is When Object-Image Approximations OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-40 z ' h Image zf f It is usually considered to be centered on centered to be It is usually considered z with either height or size. or ±h'. or ±h'. size. is half the height The hzzfz hzfhh mm h Object the optical axis with a height of ±h The approximation equations work In many cases, the object/image “size” is given. In many Another Way of Looking at the Approximation Another Way of Looking OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-41 f/z ≈ Magnification zz zf Magnification Approx. hey are very useful when the hey are very useful when –z m m ≈ z , so t f Approx. Distance f – z L length. Most imaging problems can be solved Object-Image ≈ Distance Object-Image : Image zfzfLzzfzzm Distance zz'L = z' –zL –zL z' = zz'L -f Inf Inf Inf Inf Inf -1 -2f-3f-4f 2f-5f 1.5f 1.33f 1.25f 4f 4.5f 5.33f 6.25f 3f 4f 5f 6f 2f 3f 4f 5f -1/2 -1 -1/3 -1/4 -1/3 -1/2 -1/4 -1/5 -10f-20f 1.11f 1.05f 11.11f 21.05f 11f 21f 10f 20f -1/9 -1/19 -1/10 -1/20 -100f 1.01f 101.01f 101f 100f -1/99 -1/100 Object Object-Image Approximations Distance The fractional error in these approximations is about times object distance more than 10-20 the focal with little computation. or no OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-42 hat is the image size Inverted and must be smaller mmm 10 10,000 2000 2000 ocal length lens. W detector. What is the required focal 100 100,000 zm mm 1000 1000 1000 0.0005 ( 0.0005)(10,000 ) 5 .001 .001 100,000 100 50 10 100,000 10,000 fmm zmm 2000 :1 5 hmmzz hmm zf 1000 :1 100 m h mh mm mm m h mh mm mmfmzmmmm mf mm length of the lens? mm f m is imaged with a 50 10 m object at 100 A (required detector size)? A 10 m object at 100 m is imaged onto a 10 mm a 10 m is imaged onto 10 m object at 100 A Approximation Examples OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-43 50 200 10 000 The image is larger The image is larger than the object. Inverted and must be larger ect is at 10 m. What is ect is at 10 zf m zz z ,mm mf mm a projector to produce an image on a screen an image on a projector to produce 10 m away from the projector. What focal length from the projector. 10 m away 200 10 10,000 h m ed with a 5 mm detector. The obj zm mm 200 200 200 0.0025 2,000 2 25 5 10 15 10,000 0.0025 2 000 3 000 fmm hmm zmmm 400 :1 400 5 2,000 2 hmmmm h,mm,mm 200 :1 50 mhmmm mhmmmmm m mf mm A 10 mm x 15 mm LCD display is used in 10 mm x 15 LCD A that is 2 m x 3 m is size. The screen is that is 2 m x 3 is size. lens is required? A 25 mm focal length lens is us A the maximum object size? Approximation Examples OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-44 camera with a 50 mm focal length lens. camera with a 50 [ ] a. 1 mm mm [ ] b. 5 mm [ ] c. 10 mm [ ] d. 100 A 10 m high object is located 50 m away from a m away object is located 50 10 m high A the detector in camera? large is the image on how Approximately Mini Quiz OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-45 0.001001 0.001001 10 10.01 50,000 0.1% / a 50 mm focal length lens. ' 50.05 zmm zmm Image is inverted and must be smaller must be is inverted and Image Error f z m hmh m mm f 50.05 ' 111 zz image on the detector in camera? image on zmm 50 m away from a camera with [ ] a. 1 mm mm [ ] b. 5 [X] c. 10 mm mm [ ] d. 100 This image cannot currently be displayed. Exact: This image cannot currently be displayed. A 10 m high object is located A is the large how Approximately Mini Quiz -Mini Quiz Solution OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-46
zz hh 1/2 1/2
/ / 12 2 12 1/2 tan FOV HFOV HFOV z h as seen from the optical system 1/2 as seen from the optical system stead of FOV to emphasize that this is a to emphasize stead of FOV z of an optical system defined by 1/2 z - maximum object height h the - maximum image height h' the - maximum angular size of the object the - maximum angular size of the image the h Field of View FOV: the diameter of the object/image the radius of object/image HFOV: Half field of View in is sometimes used FFOV Full field of View diameter measure. For a thin lens: The half field of view HFOV HFOV half field of view The Field of View Field of OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-47 f h Chief
1/2 1/2 1/2 tan( ) ' tan(' ) HFOV hf u h' F' lens. If the object is not on the optical lens. If the object is not on ray drawn in the diagram is called ray drawn ar diameter of the object he angular radius of the object usually expressed as an angular size: ' (the slope of the ray). zf with respect to the optical axis. Chief Ray Angle Chief Ray HFOV –HFOV Half Field of View – t FOV – Field of View – the angul 1/2 u , and is the and , Ray axis, these parallel rays are tilted image is formed at (or near) the rear focal point of system: The pupils, the central In the context of stops and A distant object produces collimated rays at the For distant scenes, the object height is For distant scenes, Field of View and Focal Length OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-48 22 HV hh f size of the object h V h for the entire scene or image separation measured as the angular y records a rectangular image. Different y records a rectangular image. Different the detector size. The optical system The the detector size. 30 degrees (HFOV = 15 degrees) 30 degrees (HFOV vertical and diagonal directions: diagonal vertical and 1/2 1/2 1/2 H ff f 1 degree = 60 arc minutes = 3600 arc seconds h tan( ) ' tan( ) 111 tan tan tan HFOV h f u HVD -of the camera is FOV the - stars two are separated by 10 arc seconds HFOV HFOV HFOV Field of View and Focal Length In a general system, the angular FOV is usually In a general system, the angular FOV These relationships These determine the image height for element in the scene: is determined by situations, the FOV In many a circular image, but the detector onl produces FOVs result in the horizontal, from the Entrance Pupil of system. as viewed OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-49 agonal could also be used) agonal mewhat matches human vision. The mewhat matches human vision. Vertical or the Di Vertical a focal length of about 40-60 mm. This mm. 40-60 a focal length of about V are called long focus lenses. are called long focus V u V are called wide angle lenses. V 2030405075 0.9 0.6 0.45 0.36 42.0 0.24 31.0 24.2 19.8 13.5 84.0 62.0 48.4 39.6 26.0 100200 0.18 0.09 10.2 5.14 20.4 10.3 1000 0.018 1.03 2.06 Focal Length (mm) (deg) HFOV (deg) FOV (Note this is the Horizontal HFOV; the HFOV; this is the Horizontal (Note produces an image perspective and FOV that so an image perspective and FOV produces degrees. 40-50 of a normal lens is about FOV FO a larger that produce Lenses Lenses that produce a smaller FO In photographic terms, a normal lens has In photographic Field of View -View Field of Example 35 mm Film – frame the size is 24 x 36 mm Use: h' = 18 mm OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 3-50 u ith the size of image format for a given get the same FOVs as with 35 mm film? as with 35 get the same FOVs 84.062.048.439.6 42.026.0 31.020.4 24.210.3 19.8 0.92.06 13.5 0.6 10.2 0.45 5.14 0.36 1.03 0.24 4.9 0.18 7.3 9.8 0.09 0.018 12 18 24 49 244 FOV (deg)FOV (deg) HFOV Focal Length (mm) angular FOV. angular FOV. The required focal length scales linearly The w Electronic Sensors –arrays CCD Example 2/3 inch format – 6.6 x 8.8 mmWhat are the required focal lengths to Use: h' = 4.4 mm Field of View -View Field of Scaling