GEOMETRIC OPTICS

1. GEOMETRIC OPTICS

2. By DR.AMER ISMAIL ABUIMARA JORADNIAN BOARD OF OPHTHALMOLOGY INTERNATIONAL COUNCIL OF OPHTHALMOLOGY PALESTINIAN BOARD OF OPHTHALMOLOGY

3. Is the study of light and images using geometric principles . • Geometric optics uses linear rays to represents the paths traveled by light .

4. PINHOLE IMAGING • Make a pinhole near the center of a large sheet of aluminum foil, light a candle , and extinguish all other illumination in the room . hold a sheet of plain white or , better ,waxed paper about 2 ft from the candle , and place the pinhole midway between the paper and the candle . observe an inverted image of the candle flame on the paper • Moving the pinhole closer to the candle while keeping the paper stationary yields a larger image.

6. An object may be regarded as a collection of points . • Geometric optics treats every point of an object as a point source of light . • An object has an infinite number of point sources , and each source point is infinitesimally small. • Light radiates in all directions from each point on an object .

7. Stars behave as point sources . the point source is mainly a conceptual tool : it is usually easier to understand an optical system by concentrating on the light radiating from a single object point or a few points .

8. For every object point , there is a specific image point . in optics the term ( conjugate ) refers to these corresponding object and image points . • A ray is a geometric construct indicating the path of light as it travels from an object point to the corresponding image point . rays represent only a path .they do not indicate The amount ( intensity ) or wavelength of light traveling along the path .

9. Usually light travels from left to right . • Pencil of light is a small collection ( bundle ) of light rays traveling in the same direction .pinhole images are usually too faint to be useful . • A solar eclipse can be safely observed with a pinhole. • Several pinholes yield several images . • The pinhole restricts the brightness not the size of the image .

10. Clinical examples for conjugate points are : • retinoscopy • direct ophthalmoscopy .

11. IMAGING WITH LENSES AND MIRRORS • Repeat the pinhole imaging demonstration , but replace the pinhole with a +6 D sphere trial lens , and note the improvement in the image . vary the distances among the candle ,lens and paper , and observe the variety of different image characteristics that can be obtained • Deferent lenses provide an even broader range of images .

13. Compared with the pinhole , the lens allows much more light from each object point to traverse the lens and ultimately contribute to the image . • Generally lenses produce better images than do pinholes .

14. What are the disadvantages of lenses ??? • image only in one location . • mirrors produce images in much the same way as lenses .

15. Most optical systems are rotationally symmetric about their long axis . this axis of symmetry is the optical axis . although the human eye is not truly rotationally symmetric , it is nearly symmetric .

16. OBJECT CHARACTERISTICS • By location with respect to the imaging system • By luminosity ( if they produce their own light . • If not they only can be imaged if they are reflective and illuminated .

17. IMAGE CHARACTERISTICS • magnification • location • quality • brightness

18. MAGNIFICATION • Three types are considered in geometrical optics : • transverse • angular • axial • the ratio of the height of an image to the height of the corresponding object is known as transverse magnification .

19. transverse magnification = image height / object height • object and image heights are measured perpendicular to the optical axis and , by convention , are considered positive when the object or image extends above the optical axis and negative , below the axis .

20. for example : if the object height is + 6cm , and the image height is -3cm , thus the transverse magnification is – 0.5 , meaning that the image is inverted and half as large as the object . • transverse magnification applies to linear dimensions . for example , a 4cmx 6cm object imaged with a magnification of 2 produces an 8cmx 12cm image . both width and length double , yielding a fourfold increase in image area .

21. generally , the multiplication sign ,X, is used to indicate magnification . • most optical systems have a pair of nodal points. • Occasionally the nodal points overlap , appearing as a single point , but technically they remain a pair of overlapping nodal points .

22. The nodal points are always on the optical axis and have an important property . • From any object point , a unique ray passes through the anterior nodal point . this ray emerges from the optical system along the line connecting the posterior nodal point to the conjugate image point .

23. These rays form 2 angles with the optical axis . • The essential property of the nodal points is that these 2 angles are equal for any selected object point . because of this feature , nodal points are useful for establishing a relationship among transverse magnification , object distance, and image distance .

24. Regardless of the location of an object , the object and the image subtend equal angles with respect to their nodal points. • Transverse magnification= image height = image distance object height object distance

25. As practical matter , object and image distances must obey a sign convention consistent with the established convention for transverse magnification . • Object distance is measured from the object to the anterior nodal point , and image distance is measured from the posterior nodal point to the image . • For a simple thin lens immersed in a uniform medium such as air , the nodal points overlap in the center of the lens .

26. ANGULAR MAGNIFICATION • Is the ratio of the angular height subtended by an object seen by the eye through a magnifying lens , to the angular height subtended by the same object viewed without the magnifying lens . • By convention , the standard viewing distance for this comparison is 25cm . • For small angles , the angular magnification provided by a simple magnifier (P) is independent of the actual object size : • M= (1/4)P or M= P/4

27. AXIAL MAGNIFICATION • Also known as longitudinal magnification , is measured along the optical axis . • For small distances around the image plane, axial magnification is the square of the transverse magnification . • Axial magnification = ( transverse magnification )2

28. IMAGE LOCATION • Refractive errors result when images formed by the eye’s optical system are in front of or behind the retina . • Image location is specified as the distance ( measured along the optical axis ) between a reference point associated with the optical system and the image .

29. The reference point depends on the situation . it is often convenient to use the back surface of a lens as reference point . the back lens surface is usually at the same location as the posterior nodal point , but it is easier to locate . • Frequently , image distance is measured from the posterior principal point to the image .

30. The principal points like the nodal points , are a pair of useful reference points on the optical axis . the nodal points and principal points often overlap . • Whatever reference point is used to measure image distance , the sign convention is always the same . • When the image is to the right of the reference point , image distance is positive ; when the image is to the left of the reference point , the distance is negative .

31. DEPTH OF FOCUS • Perform the basic imaging demonstration with a lens as described before ( imaging with lenses and mirrors ) , and notice that if the paper is moved forward or backward within a range of a few millimeters , the image remains relatively focused . with the paper positioned outside this region , the image appears blurred .

32. The size of this region represents the depth of focus , which may be small or large depending on several factors . • In the past , depth of focus was of concern only in the management of presbyopia . however , it is an important concept in refractive surgery as well .

33. Depth of focus applies to the image . depth of field is the same idea applied to objects . • If a camera or other optical system is focused on an object , nearby objects are also in focus . • Objects within the range of depth of field will be in focus , whereas objects outside the depth of field will be out of focus .

34. IMAGE QUALITY • Careful examination reveals that some details in an object are not reproduced in the image . • Images are imperfect facsimiles , not exact scaled duplicates of the original object . • Consider an object 50 cm in front of a pinhole 1mm in diameter . paper is placed 50 cm behind the pinhole , so the magnification is -1 . • A small pencil of rays from each object point traverses the pinhole aperture .

37. Each object point produces a 2-mm diameter spot in the image . these spots are called blur circles . this term is somewhat misleading because off-axis object points technically produce elliptical spots in the image . • In addition, this analysis ignores diffraction effects that make the spot larger and more irregular .

38. Regardless , each object point is represented by a blur circle in the image , and the farther the image is from a pinhole , the larger the blur circle in the image . • To the extent that these blur circles overlap , the image detail is reduced ( blurred ). • To some extent , the loss of detail is mitigated with the use of a smaller pinhole .

40. A smaller pinhole gives a dimmer , but more detailed , image . however the smaller the pinhole , the more that diffraction reduces image quality . • While a smaller blur circle preserves more detail, the only way to avoid any loss of detail is to produce a perfect point image of each object point . • Theoretically , if a perfect point image could be produced for every point of an object , the image would be an exact duplicate of the object .

41. A perfect point image of an object point is called a ( stigmatic image ) . • “ stigmatic “ is derived from the Greek word stigma , which refers to a sharply pointed stylus . • Loss of detail occurs in lens and mirror imaging as well , because light from an object point is distributed over a region of the image rather than being confined to a perfect image point .

43. Generally , lenses focus light from a single object point to a spot 10-100micrometer across . • This is better than a typical pinhole , but the shape of the spot is very irregular . • The term ( blur circle ) is especially misleading when applied to lenses and mirrors . • A better term is ( point spread function ) , which describes the way light from a single object point is spread out in the image .

44. To summarize , a stigmatic image is a perfect point image of an object point . • However , in most cases , images are not stigmatic . instead , light from a single object point is distributed over a small region of the image known as a blur circle or , more generally , a point spread function PSF . • The image formed by an optical system is the spatial summation of the PSF for every object point .

45. The amount of detail in an image is related to the size of the blur circle or PSF for each object point . • The smaller the PSF , the better the resemblance between object and image .

46. LIGHT PROPAGATION • OPTICAL MEDIA AND REFRACTIVE INDEX • Light travels through a variety of materials , such as air , glass , plastics , liquids , crystals , some biological tissues , the vacuum of space , and even some metals .

47. A medium is any material that transmits light . • Light travels at different speeds at different media . light moves fastest in a vacuum and slower through any material . • The refractive index of an optical medium is the ratio of the speed of light in a vacuum to the speed of light in the medium and is usually denoted in mathematical equation by the lowercase letter n .

48. The speed of light in a vacuum is 299,792,458m/s. this is approximately 300,000 km/s or 186.000 miles / s . • In 1983 the Systeme International defined a meter as the distance light travels in a vacuum during 1/299,792,458 of a second . • Refractive index is always greater than or equal to 1 .

49. In computations , it is often easier to work with the refractive index of a material than directly with the speed of light . • n = speed of light in vacuum speed of light in medium

50. refractive index is quite sensitive to a material’s chemical composition . • a small amount of salt or sugar dissolved in water changes its refractive index . • because refractive index is easy to measure accurately , chemists use it to identify compounds or determine their purity . • glass manufacturers alter the refractive index of glass by adding small amount of rare earth elements . • until recently , clinical labs screened for diabetes by measuring the refractive index of urine .