KMK Optics (Geo + Physio)

wavelengths and chromatic aberrations and how they are used in clinic

"blue bends best" shorter wavelengths bend more than longer wavelengths utilized with R/G balance *diffraction gratings are opposite (red bends better than blue)

radius of curvature for a mirror

( = -r ) = +r "only need a C- for mirrors" *opposite of lenses

radius of curvature for a lens (negative vs. positive)

( shaped = +r <-- "need at least a C+ in lenses" ) shaped = -r

ANSI tolerance of axis: 0.25D or less >0.25-0.50 >0.50-0.75 >0.75-1.50 >1.50D

0.25D or less = +/- 14 >0.25-0.50 = +/- 7 >0.50-0.75 = +/- 5 >0.75-1.50 = +/- 3 >1.50D = +/- 2

calculating pd given degrees of deviation

1 degree of deviation = 1.75pd

spherical equivalent equation

1/2cyl + sphere power +3.00-2.00x180 --> +2.00D

magnification of a 60D vs. 78D vs. 90D lens

60D = -1x <-- inverted and true size 78D = -0.77x <-- inverted and minified 90D = -0.67x <-- inverted and minified (smallest image) *55D Hubry lens = +1.09 <-- upright and magnified

ANSI tolerance of cyl power of lenses: <2D >2-4.50D >4.50D

<2D = +/- 0.13 2-4.50D = +/- 0.15 >4.50D = +/- 4% of cyl power

ANSI tolerance of sphere power of lenses: <6.50D >6.50D

<6.50 = +/- 0.13D >6.50 = +/- 2% of the lens power

how to calculate frame pd of a lens (aka distance between geometrical centers)

A + DBL

A vs. B measurement of a lens DBL

A = horizontal measurement of a lens B = vertical measurement of a lens DBL = distance between lenses

use of the following lasers in clinic: Argon Nd: YAG Excimer Argon Krypton

Argon = panretinal photocoagulation (PRP), argon laser trabeculoplasty (ALT), and peripheral iridotomy (LPI) Nd: YAG = selective laser trabeculoplasty (SLT), posterior capsulotomy, and laser peripheral iridotomy (LPI) Excimer = PRK and LASIK Krypton = same as Argon (PRP, ALT, LPI

BIO vs. DO: FOV, mag, and image created

BIO = larger FOV, less magnification, and real and inverted image DO = smaller FOV, more magnification, and virtual and upright image

how CL Rx relate to spectacle Rx

CL Rx = ALWAYS more PLUS (+) than spectacle Rx <-- for myopes and hyperopes *hyperopes -- CL become weaker (more minus) the closer to the cornea they get (need more plus to make up the difference) *myopes -- CL get more minus the closer to the cornea they get (need more plus power to take away the difference)

n and abbe # of these materials: Crown glass CR-39 Polycarb Trivex

Crown glass -- 1.523 and 58.9 <-- heaviest CR-39 -- 1.498 and 58 Polycarb -- 1.586 and 30 <-- high chromatic aberration Trivex -- 1.53 and 44 <-- lightest

lensometry

Equation: x = (f^2)F *f = focal length of standard lens in meters *F = back vertex power of lens *x = amount moved on dial (target away = (-) and target towards = (+)) single line (3 tiny lines together) = sphere power triple lines (3 large lines separated) = cyl power *start w/ power drum all the way in the plus (rotated toward you) -- move the drum away from you, if the triple lines come into focus first, need to flip axis drum 90 degrees *moving power away from you = "moving" object away <-- more negative *moving power drum toward you = "moving" object toward <-- more positive

SSRI equation

F = (n2-n1)/r *n2 = final medium *n1 = initial medium *r in m if given radius of back and front, treat each surface like an SSRI and then add powers together

converting keratometry readings to base curve and vice versa

F = 0.3375/r <-- r in m or... F = 337.5/r <-- r in mm

equation for mirror power

F = 2n/r

calculating sag when n is different than the n lens clock calibrated for

FL = ((nL-1)/(nLc-1))Flc ex: clock calibrated for 1.5 lens = 1.7 +6D lens ((1.7-1)/(1.5-1))6 = +8.40D lens

OC of these segment types: FT 28 (or less) FT 35 Executive Round segs Ribbon R-segs

FT 28 (or less) = 5mm FT 35 = 4.5mm Executive = 0mm Round Seg = 1/2 of given value (i.e. you will be given Round Seg 22 = 11mm) Ribbon R-segs = 7mm

CL vertex equation

Fcl = F/(1-dF) *d = vertex change in meters *same as effective vergence equation (use lens power instead of vergence) if calculating from CL --> Spectacle, then -d value

equivalent power equation

Feq = F2+F1-(t/n)(F1)(F2) *approximation of a thick lens' power *t = thickness of the lens in meters *n = lens index of refraction

how to calculate lens decentration

Frame pd - pt. pd = total decentration must divide by 2 to get decentration per lens

back vertex and equation

Fv = F2 + F1/(1-(t/n)F1) *back vertex = the Rx of a spectacle lens *n = index of the lens *what creates the vergence of light leaving a lens *very similar to vertex equation but must add back surface power and account for t and n

minimum blank size equation

M = ED + 2(d) + 2 d = decentration in a single lens in mm

how we measure depth of focus in clinic

MEM <-- measuring accuracy of accommodation (lag and lead)

match laser type w/ action: Nd:YAG laser Excimer laser Tunable dye laser Carbon dioxide laser Argon laser

Nd:YAG laser -- photodisruption "FAGs are super disruptive" Excimer laser -- photoablation "excimer sounds like excited, ablation sounds like elation" Tunable dye laser -- photoradiation "you dye from radiation" or "you tune a radio" Carbon dioxide laser -- photoevaporization (vaporizes into water) Argon laser -- photocoagulation (denatured proteins)

most concerning monochromatic aberrations

OCD = Oblique, Curvature of field, and Distortion

curve that allows us to select the best bast curve to eliminate oblique astigmatism and curvature of field

Oswalt curve on the Tscherning ellipse <-- leads to a flatter lens overall *can only fix one or the other (astigmatism or cof)

power of 2 thin lenses together

P = P1+P2 *add thin lens powers together (no special equations required)

general vergence equation

V = U+P

effective vergence equation (vergence change w/ some distance)

Veff = V/(1-dV) *d in meters *V = vergence given *Veff = vergence of that light after some distance traveled (different b/c all light loses vergence as it travels away from an object)

how do polarizers work

absorb light along the axis 90 degrees from their orientation Ex: sunglasses w/ vertical polarization grating will absorb horizontal light

how to transpose from +cyl to -cyl

add sphere and cyl powers flip sign of cyl flip axis 90 degrees +3.00+2.00x090 --> +6.00-2.00x180

3 things that determine the quality of an image

brightness (AS) <-- # of rays getting to the image clarity field of view (FOV) <-- which object rays reach the image

prentice's rule for an oblique lens/eye shift

calculate both vertical and horizontal component to determine vertical and horizontal prism induced

prentice's rule

calculates induced prism pd = dF d in cm

achromatic doublet

combination of + and - lens to minimize chromatic aberrations F1 = (abbe1/(abbe1-abbe2))Ftotal

concave vs. convex lens

concave = wraps around lower medium (n) (a cave is rock but wraps around air) convex = wraps around higher medium (n)

aberrations that distort image plane

curvature of field distortion *all are monochromatic aberrations

Necessary thickness of AR coating given wavelength and n of the AR coating and equation for finding n of AR given a material n

d = lambda/4/n or lambda/n/4 *n of AR * if no wavelength specified, use 555nm Ex: 530nm light incident on an AR coating (n= 1.32). Thickness needed? 530/4/n = 100.4nm *n of AR coating must be less than n of spectacles material of n1, what is AR n? -- sqrt(n1*air) = n AR

snell's law

describes the relationship between light entering a medium and how it refracts (bends) light into higher n = slows down = bends toward normal light into lower n = speeds up = bends away from normal

4 prism equations

deviation power: pd = y(cm)/x(m) deviation angle: d = A(n-1) <-- A = apex angle in degrees and d is in degrees <-- and 1 degree = 1.75pd; 1 in equation is n of surrounding substance (different if submerged in water for instance) thickness: pd = 100((thickness difference*(n-1))/length of prism) decentration: pd=dF (d in cm)

seg inset

difference between distance pd and near pd distance pd - near pd = overall seg inset divide by 2 for seg inset per lens

inset

difference between frame pd and pt.'s distance pd frame pd - distance pd = overall inset divide by 2 for inset per lens

total inset

difference between frame pd and pt.'s near pd frame pd - near pd = overall total inset divide by 2 for total inset per lens

diverging vs. converging lenses

diverging = spreads out light <-- always a concave surface of the lens converging = brings light to focus <-- always a convex surface of the lens

measuring prism on lensometry

each ring = 1pd (3 away from center = 3pd) Base is wherever the crossed lines fall on the grid --> if OD lens, crossed lines to the left = BO --> if OS lens, crossed lines to left = BI etc.

lateral (transverse) chromatic aberrations

each wavelength creates a different image size

longitudinal (axial) chromatic aberratoins

each wavelength is bent differently by a lens and is imaged at different locations

field of view (FOV) and difference between (+) and (-) lenses

extent of an object plane that is imaged + = decreased FOV - = increased FOV <-- how reverse telescopes work w/ low vision

flat vs. steep cornea w/ keratometry

flat = larger radius = larger image steep = smaller radius = smaller image *flatter = smaller numbers (less powerful) *steeper = larger numbers (more powerful) 42@90 and 45@180 <-- 45 = steeper which gives ATR cornea Rx = plano-3.00x090

hard vs. soft progressive designs

hard = short corridor and/or high add power soft = long corridor and/or low add power

ANSI tolerance for vertical and horizontal prism horizontal <2.75D sphere vertical <3.375D sphere

horizontal <2.75D sphere = 0.67 <-- 2/3pd vertical <3.375D sphere = 0.33 <-- 1/3pd

apparent depth problems

if surface has no power (P=0) then solve as a proportion: n1/v = n2/u <-- solve for the image location

exit pupil (XP)

image of the AS formed by all lenses behind the AS *if no lenses behind the AS, the AS is the XP

entrance pupil (EP)

image of the AS formed by all lenses in front of the AS *if no lenses in front of AS, the physical AS is the EP

exit port

image of the FS formed by all the lenses behind it * if no lenses behind it, the FS is the exit port

entrance port

image of the FS formed by all the lenses in front of it * if no lenses in front of it, the FS is the entrance port

depth of focus

interval in front and behind the retina where an object will still be seen as clear

relationship between abbe # and chromatic aberration

larger abbe # = less chromatic aberrations <-- inversely proportional CA = F/abbe# if given dispersive power, 1/dispersive power = abbe # --> then use in regular equation

field stop (FS)

limits the size of an object that can be viewed by the system (works in conjunction w/ AS)

what is the nodal point

location where light enters and exits a lens undeviated --- center of curvature for a simple lens *solve these equations by creating a proportion nodal points and principle plane are the same location in a thick lens

chromatic aberrations (non-monochromatic)

longitudinal (axial) lateral (transverse)

lateral magnification equations

m = hi/ho = U/V = v/u *v/u only works if both u and v are in the same medium (n=n)

radiuscope and how it works

measures the radius of curvature of an RGP two clear image loactions (back focus and front focus) --> difference between focus points = radius of curvature

keratometer

measures the radius of curvature of the cornea treats the cornea like a convex mirror (diverging mirror)

lens clock

measures the sag of a lens

power of a spherocylindrical lens at an oblique axis

midway power (draw on optical cross) at a midway axis +5.00-2.00x135 --> +5@135 and +3@45 --> oblique power = +4@90

movement seen w/ hand neutralization

minus lens = with -- need to neutralize w/ + plus lens = against -- need to neutralize w/ -

6 digit code of n and abbe # Ex: 569-561

n = 1.569 abbe # = 56.1

equation relating image ad object location to vergence

n/v = V n/u = U *n = medium that the light is traveling in

radial/oblique astigmatism aberrations

occurs w/ rays hitting the lens at an angle creates T, S, and P image planes (teacup, saucer, and plate) corrected by base curve corrected by point field

coma aberrations

off axis points get imaged in a way that creates an image tail toward the axis corrected by the eye

spherical/longitudinal aberrations

paraxial and non-paraxial rays experience varied magnification = some rays imaged closer to the lens than others = blur circle contributes to night myopia (along w/ larger pupils = decreased depth of focus) corrected by the eye in high powered lenses, corrected by aspheric lenses

curvature of field aberrations

peripheral defocus -- edges of an image plane are blurred may lead to myopia progression corrected w/: -curved screen -base curve -percival form

aperture stop (AS)

physical entity limiting light entering the system

what test in clinic improves depth of focus

pinhole -- extends range and allows for more clarity of an object

ANSI high mass impact testing

pointed projectile 500 grams dropped from 50 inches

primary vs secondary focal point

primary = location where an object creates parallel rays leaving the lens interface secondary = where parallel light entering the lens interface creates an image <-- what we generally think of as the lens' focal point

depth of field

range in space where an object is seen as in focus *think about range of clear vision in presbyopes w/ an add

base curve of spectacles vs. CL

spectacles -- bc typically on front surface CL -- bc typically on back surface

aberrations that distort image quality

spherical/longitudinal coma radial/oblique astigmatism *all are monochromatic aberrations

ANSI high velocity impact testing

steel ball -- 0.25 inch diameter fired at 150 fps

distortion aberrations

straight line objects create straight images when rays go directly through the center of the lens plus lens = pinchushion minus lens = barrel corrected by orthoscopic doublet (combination of lenses)

If F1 is positive (+), how does back vertex (Fv) change w/ changes in t and n

t increase = more positive Fv (stronger) index (n) increase = less positive Fv (weaker

If F1 is negative (-), how does back vertex (Fv) change w/ changes in t and n

t increase = more positive Fv (weaker) index (n) increase = less positive Fv (stronger)

effective diameter

the diameter of the largest portion of the lens (can be A, B or oblique measurement)

circle of least confusion

the dioptric midpoint of the powers of each meridian *if 180 is +2D and 90 = +1D...COLC = +1.5D

sag of a lens

the distance from the center of the lens to the chord (imaginary line from edge to edge) to the surface of the lens

interval of sturm

the linear distance between the focal points of each meridian *if +2D and +3...linear distance between 50cm and 33cm = ios of 17cm

AS of the eye

the pupil

using a lens clock to measure a RGP lens based on center thickness

thickness given in mm can determine both power in D and in mm *for D, multiply by 10 --> 0.25mm = 2.5D *for mm, move decimal to the right one unit --> 0.25 = +2.5mm Ex: -if lens clock reads 0.25mm then... D = 0.25*10 = +2.5D -if lens clock reads 0.25mm then... mm = +2.50mm

pantoscopic tilt and how it changes the power of a lens (+ vs. -)

tilt of the lens around the 180 axis *always adds cyl to that axis (180) of the same power as the lens -plus lens w/ panto would add +cyl in 180 axis -minus lens w/ panto would add -cyc in 180 axis

faceform tilt and how it changes the power of a lens (+ vs. -)

tilt of the lens around the 90 axis "royal wave" *always adds cyl to that axis (90) of the same power as the lens -plus lens w/ faceform would add +cyl in 90 axis -minus lens w/ faceform would add -cyc in 90 axis

total internal reflection and the critical angle

total internal reflection = when all light w/in a medium is reflected off the surface and cannot be refracted through --- only occurs when light goes from higher n to lower n (bends so much away from normal that just get reflected w/in) total internal reflection occurs when angle of incidence > critical angle critical angle = angle at which light traveling to a surface will be reflected internally (cannot leave the medium)

Munnerlyn's formula

used w/ LASIK to calculate ablation need based on RE and optical zone ablation depth = (OZ^2*RE)/3 in general, ~15microns/D for LASIK *OZ in mm and absolute value of RE

metastable state in lasers

when atoms have a short life in the highest state but a very long life in the excited state -- allows for population inversion to occur

population inversion in lasers

when there are more atoms in an excited state than in a ground state -- allows for stimulated emission to occur