Parte 2: ottica geometrica INO - CNR Istituto Nazionale di Ottica www.ino.it 2011 Nozioni base di Ottica Parte 2: ottica geometrica Relatori: Luca Mercatelli David Jafrancesco CNR - INO Largo Fermi 6, 50125 Firenze Tel. +39 055 23081 - Fax +39 055 2337755

Introduzione L’ottica può essere idealmente suddivisa in tre campi differenti che richiedono metodologie e trattazioni diverse. ottica geometrica (trattata con il metodo dei raggi di luce) ottica fisica (trattata con la teoria delle onde) ottica quantistica (trattata con i metodi della meccanica quantistica) L’ottica geometrica spiega i fenomeni di trasmissione, riflessione e rifrazione L’ottica fisica spiega i fenomeni di interferenza, diffrazione e polarizzazione Diaframma di fronte a sorgente puntiforme: limite di diffrazione Laboratorio di Fotometria e Illuminotecnica 2

Elementi di Ottica Geometrica L’ottica geometrica consiste nel trovare il cammino, attraverso i sistemi ottici, dei raggi luminosi, immaginati come linee geometriche lungo le quali fluisce l’energia. Si basa su poche osservazioni di carattere sperimentale Esempio TracePro: Lightpipe semplice Nei mezzi omogenei la luce, intesa come sottili fasci (raggi), si propaga in linea retta. Le leggi di rifrazione e riflessione Raggi di luce diversi non si perturbano vicendevolmente durante la propagazione né interferiscono tra di loro. Laboratorio di Fotometria e Illuminotecnica 3

Riflessione La riflessione ha luogo ogni volta che un raggio luminoso incontra una superficie, essa può essere: interfaccia di separazione tra due mezzi trasparenti (di indice di rifrazione diverso) superficie che delimita un corpo opaco. Le leggi fondamentali della riflessione possono essere enunciate come segue: Il raggio incidente ed il raggio riflesso giacciono sullo stesso piano L’angolo di incidenza è uguale all’angolo di riflessione, dove per angolo di incidenza/riflessione si intende l’angolo formato dal raggio incidente/riflesso con la normale alla superficie. Laboratorio di Fotometria e Illuminotecnica 4

Riflessione Le superfici levigate possono essere piane o curve, si ha così una prima distinzione tra specchi piani e curvi, dunque questi ultimi oltre ad essere concavi o convessi possono avere forma sferica, ellittica o parabolica in una o due dimensioni. Il raggio luminoso parte dal punto oggetto P, posto a distanza D dallo specchio, viene riflesso per essere infine rivelato (occhio). L’immagine P’ del punto P è un’immagine virtuale (non reale, formata dai prolungamenti dei raggi luminosi e non dai raggi stessi) posta ad una distanza 2 D dal punto P stesso. Laboratorio di Fotometria e Illuminotecnica 5

Rifrazione Ogni volta che un raggio luminoso incide sulla superficie di separazione tra due mezzi, oltre ad avere una parte del raggio riflessa, si ha che una parte viene del raggio viene rifratto nel secondo mezzo. La legge della rifrazione, nota come legge di Snell, può essere enunciata come segue: il raggio rifratto giace nel piano individuato dal raggio incidente e dalla normale alla superficie il rapporto tra il seno dell’angolo di incidenza e quello di rifrazione stanno in rapporto costante: Laboratorio di Fotometria e Illuminotecnica 6

Rifrazione Nel caso in cui la superficie di separazione costituisca l’interfaccia tra aria ed un mezzo trasparente, ed il raggio, incidendo sulla superficie, venga rifratto all’interno del mezzo, la costante nell’equazione prende il nome di indice di rifrazione n del mezzo Se l’angolo di incidenza è abbastanza piccolo in modo da poter sostituire il seno dell’angolo con l’angolo stesso, si ottiene infine Laboratorio di Fotometria e Illuminotecnica 7

Lenti Le lenti possono essere pensate come due diottri* uniti insieme; e le combinazioni dovute alla curvatura dei due diottri danno luogo alle due tipologie di lenti: convergenti e divergenti *diottro: superficie sferica di separazione tra due mezzi di indice di rifrazione diverso Il punto focale primario F è un punto sull’asse ottico avente la proprietà che ogni raggio emergente da esso che incide sulla lente, dopo la rifrazione emerge parallelamente all’asse ottico.  Il punto focale secondario F’ è un punto sull’asse ottico avente la proprietà che ogni raggio che si propaga parallelamente all’asse ottico ed incide sulla lente, dopo la rifrazione emerge diretto verso tale punto. Laboratorio di Fotometria e Illuminotecnica 8

Lenti Laboratorio di Fotometria e Illuminotecnica 9

Lenti Laboratorio di Fotometria e Illuminotecnica 10

Sistemi di lenti (obiettivi) Laboratorio di Fotometria e Illuminotecnica 11

The Lens 12 Laboratorio di Fotometria e Illuminotecnica Slide objective: To introduce lenses and lens terminology Speaker text: The remainder of this presentation will be about lenses and lens terminology and the different objects a lens is made up of Picture: The image illustrates some of the terms an elements that will be discussed in the remaining part of this presentation Laboratorio di Fotometria e Illuminotecnica 12

Angle of view Same as “Field of view” Slide objective: To introduce the term Field of view Speaker text: Field or Angle of View is the part of the scene visible with a particular lens. Lenses that provides a wide angle of view are normally called wide angle lenses, lenses with a narrow angle of view are called telephoto lenses (or “tele lenses for short”). The Angle of view is commonly measured horizontally, vertically or diagonally. Pictures: The images illustrates horizontal and vertical angle of view Same as “Field of view” What the camera with a given lens can “see” Horizontal, vertical or diagonal Laboratorio di Fotometria e Illuminotecnica 13

Lenses - Focal length A small focal length gives wide angle view. Slide objective: To explain the term focal length Speaker text: Parallel incident light transmitted into a convex lens converges to a point on the optical axis. This point is the focal point of the lens. (normally by the image sensor) The distance between the principal point in the optical system and the focal point is referred to as the focal length. For a single thin lens, the focal length is equal to the distance between the center of the lens and the focal point. The focal length of a lens determines its angle of view at a given distance. A lens with a short focal length has wide-angle characteristics while a lens with long focal length has telescopic characteristics Picture: The image illustrates the principle of focal length. A small focal length gives wide angle view. A large focal length gives tele view. Laboratorio di Fotometria e Illuminotecnica 14

Lenses – Depth of field Slide objective: To introduce and explain the term depth of field Speaker text: The focus ring on a lens is usually adjusted so that the object of interest within the scene is sharp. Up to a certain point, objects in front of this setting, and behind it, are in focus as well. This zone of focus is referred to as the Depth of Field. As objects get further outside of the depth of field (either further from the lens or closer to it), they will lose focus. The depth of field also varies with the focal length of the lens. Wide angle lenses (i.e. those with short focal lengths) have a greater (deeper) depth of field than telephoto types. Picture: The image illustrates the depth of field of a camera configuration note that only about 40% of the “men” standing behind and in front of the man that is in the “focus point” in focus remains sharp and clear. The regions in front of and behind the focus point where the image remains in focus Laboratorio di Fotometria e Illuminotecnica 15

Entrance pupil diameter/focal length Lenses - Aperture F-number: Entrance pupil diameter/focal length Slide objective: To introduce and explain the term Aperture Speaker text: Another important factor affecting the image a lens produces is the lens Aperture (The “opening” of a lens) It indicates the measure of the lens light gathering capability. Relative Aperture is a ratio between its focal length and effective aperture and is measured in F numbers or F-stop values e.g. F1.4, F1.3, etc. Generally, the lower the F-stop, the more light gathering capability the lens has. Advanced (optional) text: The f-number of a lens is the ratio of the focal length to the effective object lens diameter. It is a mechanical ratio and does not infer the efficiency of a lens. It does affect the amount of light energy passed to the sensor and will play a significant part in the resulting picture. In simple terms the smaller the f-number the more light is passed to the sensor, therefore f1.2 is better than f1.8. The percentage of light passed by different apertures is listed in the table. This shows the percentage of light falling on the lens that is passed to the image sensor. Picture: The diagram above illustrates the amount of light that is passed to the image sensor at sample F-values Table : The Table illustrates the amount in % of light that is passed to the image sensor at sample F-values F number f1.0 f1.2 f1.4 f1.7 f2.8 f4.0 f5.6 % of light passed 20% 14.14% 10% 7.07 2.5% 1.25% 0.625% Laboratorio di Fotometria e Illuminotecnica 16

Lenses- Mount standards CS-mount 12.5mm from camera edge to sensor C-mount 17.5mm from camera edge to sensor Conversion C to CS is possible Slide objective: To present the 2 most common mount standards for lenses Speaker text: The two most common mount standards for CCTV lenses are called C & CS mount The difference between C and CS mount equipment is the distance between the flange of the lens (the part of the case that butts up against the camera) and the focal plane of the lens (where the CCD sensor must be positioned). This is known as the flange back distance. On C mount lenses this is 17.526 mm and on CS mount lenses it is 12.5mm. Therefore if you have a CS mount camera and a C mount lens you can add a 5mm spacer to obtain the correct focus. If, however, you have a C mount camera and a CS mount lens correct focus cannot be achieved. Some C mount cameras do allow you to swap the whole mount from C to CS or vice versa. C is in many ways an old standard within CCTV it has been replaced by CS. (C-mounts is however frequently used within manufacturing applications) A 5mm spacer can be used to convert a C-lens to a CS-lens All Axis cameras with exchangeable lenses are CS-mount cameras Laboratorio di Fotometria e Illuminotecnica 17

Lenses – Sensor dependency The lens must make an image circle large enough to cover the sensor Larger sensor = more expensive lens The size (e.g. 1/3”) can not be measured anywhere. corresponds to old TV camera tubes Low end lenses produces unsharp corners Slide objective: To explain the dependency between the lens choice and the image sensor Speaker text: CCDs (and other image sensors) are usually rectangular with a 4:3 aspect ratio. Lenses are usually circular . When you put a circle over a rectangle - you must "waste" either part of the rectangle or the lens. Usually you waste part of the lens - making a circle of light larger than, and concentric to, the CCD. Image sensors are measured in "sizes", such as 1/4,1/3, 1/2, 2/3, and 1 inch. These sizes are not the diagonal length of the CCD - they are sizing standards actually originating back in the 1950's and the time of Vidicon tubes. replaced in the 60’s by CCD’s It is possible to use a lens designed for a larger sensor on a smaller sensor but not the opposite The lens must make an image large enough to cover the sensor. (If not, the corners of the image will be black.) Larger sensor equals more expensive lens Low end lenses make unsharp corners. Picture: The image is a model of a image sensor with a a suitable “lens circle” Laboratorio di Fotometria e Illuminotecnica 18

Lenses - Resolution Slide objective: To introduce and discuss the term lens resolution Speaker text: Lenses also has a resolution… Image sensors, Monitors, and lenses share one common denominator they all have a resolution measurable either in “lines” (TV/analogue measurement) or in pixels (computer related measurement). The lens resolution are normally measured in lines/mm. A typical CCTV lens has a resolution of 100 lines/mm. (In the center. Maybe 50 lines/mm at the corners.) Megapixel sensors typically have a pixel size of 3-8um, i.e. they need a lens with 200-300lines/mm. These lenses are rare and expensive. Lenses in many digital still image cameras are not as good as they should be. normally the datasheet focuses on the resolution of the image sensor and ”forgets” the important lens – No optical system is better than it’s weakest part... Picture: The image here does not have direct correlation with the subject,of the slide it is another way of demonstrating the lens size and the sensor dependency (discussed in the previous slide). A typical CCTV lens has a resolution of 100 lines/mm. Laboratorio di Fotometria e Illuminotecnica 19

Modulation Transfer Function (MTF) The MTF is a measure of the quality of contrast between features. As features move closer together, diffraction affects cause their Airy disks to begin to overlap, changing the degree of intensity between the two features. Generally, a MTF>0.5 is needed. Smaller values limit the minimum feature size Laboratorio di Fotometria e Illuminotecnica 20

Modulation Transfer Function (MTF) Laboratorio di Fotometria e Illuminotecnica 21

Lenses – Types: Wide angle Large angle of view Good in low light Good depth of field Slide objective: To introduce the wide angle lens type Speaker text: Wide angle lenses have a large angle of view giving a ”larger view” of the scene other significant factors are: Short focal length giving them deeper (greater) depth of field Normally a low F-value giving them good low-light characteristics The short focal lenght makes wide-angle lenses innapropriate on long distances The strong curvature of the lens element can create ”´barrel distortion” especially in the edges of the image (We will see a example of this on the next slide). Images: Left image shows the principle of a wide-angle lens with short focal length and a large glass area capable of gathering lots of light from a wide angle The right image is a photograph of a wide-angle CCTV-lens. “Barrel” distortion Not for long distances Laboratorio di Fotometria e Illuminotecnica 22

Lenses – Types: Telephoto Good on long distance No barrel distortion Slide objective: To introduce the telephoto (tele) lens type Speaker text: TELEPHOTO lenses - Telephoto is a term used to describe lenses that have a high focal number (length) causing the reproduced image to appear larger than human eye reproduction. They are normally used when the surveillance object is either small or far from the camera. Significant factors: Long focal length Narrow angle of view Normally a high F-stop value giving limited low-light characteristics and a shallow (smaller) depth of field Images: Left image shows the principle of a ”tele” lens with long focal length and a narrow angle of view giving limited light gathering capability The right image is a photograph of a extreme telephoto lens. Shallow (small ) depth of field Bad in low light Laboratorio di Fotometria e Illuminotecnica 23

Lenses – Macro lens Macro photography is close-up photography of usually very small objects. The classical definition is that the image projected on the "film plane" (i.e., film or a digital sensor) is close to the same size as the subject Slide objective:To briefly introduce the special lens type: ”Fish eye lens” Speaker text: Extremely wide angle lenses are called ”Fish eye lenses.” They are expensive as the front lens has to be very large. (Lenses are polished and it is difficult to get such a large surface good.) Images: The right image is a example of a fish eye lens, the left image is an example image taken with a fish-eye lens. Laboratorio di Fotometria e Illuminotecnica 24

ABERRATIONS Aberrazione: caratteristica o difetto della lente o del sistema di lenti (obiettivo) che porta ad alterazioni non volute dell’immagine Laboratorio di Fotometria e Illuminotecnica 25

Classifications of Aberrations Chromatic vs. Monochromatic Depends on the material of the lens Requires the beam of light to contain more than one wavelength In Focus vs. Out of Focus Out of focus aberrations cause fuzzy images where clear sharp images should be In focus aberrations cause images to be the wrong shape (distorted). Laboratorio di Fotometria e Illuminotecnica 26

Classifications of Aberrations In Focus vs. Out of Focus Out of focus aberrations cause fuzzy images where clear sharp images should be In focus aberrations cause images to be the wrong shape (distorted). Laboratorio di Fotometria e Illuminotecnica 27

Classifications of Aberrations On Axis vs. Off Axis On axis aberrations effect vision when looking straight ahead through the lens. Off axis aberrations effect peripheral vision. Wide Beam vs. Narrow Beam Wide beam aberrations depends on the lens aperture. Laboratorio di Fotometria e Illuminotecnica 28

Lens Aberrations Chromatic Spherical Astigmatism Coma Curvature of Field Distortion Laboratorio di Fotometria e Illuminotecnica 29

Chromatic Aberration The lens material breaks white light into its component colors Why? Index of refraction varies by wavelength. Laboratorio di Fotometria e Illuminotecnica 30

Chromatic longitudinal (axial) The placement of the various focal points on the axis. This is the source of the Abbé value Laboratorio di Fotometria e Illuminotecnica 31

Chromatic lateral (magnification) Different image sizes Result in colored ‘ghost’ images Laboratorio di Fotometria e Illuminotecnica 32

Chromatic Aberration Material dependent. Results in out of focus image. wearer complains of peripheral color fringes (more pronounced off-axis). The higher the power of the lens, the more the chromatic aberration. Laboratorio di Fotometria e Illuminotecnica 33

Chromatic Aberration Abbé value index Crown glass 58 1.523 PGX 57 1.523 Spectralite 47 1.537 1.6 PGX 42 1.60 Polycarbonate 30 1.586 Brooks & Borish, Systems for Ophthalmic Dispensing 2nd ed., page 503 Laboratorio di Fotometria e Illuminotecnica 34

Lens Aberrations Chromatic Spherical Astigmatism Coma Curvature of Field Distortion Laboratorio di Fotometria e Illuminotecnica 35

Spherical aberration Spherical lens: Peripheral rays have shorter focal length than paraxial rays. Laboratorio di Fotometria e Illuminotecnica 36

Spherical aberration Peripheral rays refract more than paraxial rays. Correct with parabolic curves, aplanatic lens design. Results in out-of-focus image. Wide beam aberration On-axis aberration. Laboratorio di Fotometria e Illuminotecnica 37

Lens Aberrations Chromatic Spherical Astigmatism Coma Curvature of Field Distortion Laboratorio di Fotometria e Illuminotecnica 38

Astigmatism Spherical lens, narrow beam entering off-axis. 39 Laboratorio di Fotometria e Illuminotecnica 39

Astigmatism Narrow beam aberration Also called Oblique astigmatism or Radial astigmatism. Laboratorio di Fotometria e Illuminotecnica 40

Lens Aberrations Chromatic Spherical Astigmatism Coma Curvature of Field Distortion Laboratorio di Fotometria e Illuminotecnica 41

Coma Image – cone or comet shaped.  Object, way off to the left) 42 Laboratorio di Fotometria e Illuminotecnica 42

Coma Wide beam aberration Corrected with parabolic curves, aplanatic lens design. Results in out-of-focus image. Off-axis aberration Laboratorio di Fotometria e Illuminotecnica 43

Lens Aberrations Chromatic Spherical Astigmatism Coma Curvature of Field Distortion Laboratorio di Fotometria e Illuminotecnica 44

Curvature of field Plane of focus when Marginal astigmatism is corrected Plane of focus when Curvature of field is corrected Laboratorio di Fotometria e Illuminotecnica 45

Curvature of field Also called power error. Light does not focus on a flat focal plane. The focal plane is curved. Remember the screens at drive-in movies? They are curved, not flat, to focus the sides of the movie as well as the center. The retina at the back of your eye globe is not a flat plane. It is curved. Laboratorio di Fotometria e Illuminotecnica 46

Lens Aberrations Chromatic Spherical Astigmatism Coma Curvature of Field Distortion Laboratorio di Fotometria e Illuminotecnica 47

Distortion Image is in focus, but not shaped the same as the object. Distortion – pincushion – high plus lens Laboratorio di Fotometria e Illuminotecnica 48

Distortion Object: Distortion – barrel – high minus lens 49 Laboratorio di Fotometria e Illuminotecnica 49

Distortion Brooks Systems for Ophthalmic lens Work, 2nd ed, page 509 Laboratorio di Fotometria e Illuminotecnica 50

Lens Aberrations Chromatic --------------- material dependent Spherical (the rest are not) Astigmatism Coma Curvature of Field Distortion ----------------- in-focus image (the rest give blurred images) Laboratorio di Fotometria e Illuminotecnica 51

Lens Aberrations Chromatic Spherical wide beam Astigmatism narrow beam Coma wide beam Curvature of Field narrow beam Distortion Laboratorio di Fotometria e Illuminotecnica 52

Lens Aberrations Chromatic Spherical on-axis Astigmatism off-axis Coma off-axis Curvature of Field on-axis Distortion Laboratorio di Fotometria e Illuminotecnica 53