Retinal Mag & Absorptive Lenses

Relative Mag

• Spectacle Mag

  • Compares retinal image size corrected vs. uncorrected

  • SM = l_glasses/l_uncorrected

    • Image size with glasses/image size without glasses

  • SM for thick lenses

    • SM = (shape factor) x (power factor)

      • Shape factor = 1/1-(t/n)F₁

        • t: central thickness of lens (m)

        • n: index of refraction

        • F₁: front surface power of lens

      • Power factor = 1/1-hF_v

        • h: vertex distance (m)

          • Distance between back of lens and entrance pupil of eye (m)

          • Take entrance pupil distance to cornea to be 3 mm if not specified

          • To get h, add vertex distance to distance between pupil and cornea (3 mm), and convert to m

        • F_v: back vertex power of lens

          • Back vertex power is just the power of the lens

          • Equation should tell you front vertex power separately

      • Whatever you get when you multiply shape factor and power factor tells you how much bigger image is with specs

        • Ex: if shape factor x power factor = 1.31, image is 31% bigger with specs

    • For plus lenses:

      • Increasing vertex distance (h), thickness (t), and BC (F₁₎ increases SM

      • Increasing n decreases SM

    • For minus lenses:

      • Increasing thickness and BC increases SM

      • Increasing vertex distance and n decreases SM

    • Increasing thickness and BC always increases SM

    • Increasing n always decreases SM

    • Increasing vertex distance increases SM in (+) lenses (why presbyopes pull lenses away from face) and decreases SM in (-) lenses

  • Relative Spectacle Mag (RSM)

    • Compares retinal image size corrected vs. retinal image size on an emetrope

      • Retinal image size corrected relative to standard eye

    • RSM = I_a/I_s

      • Image size in an ametrope/image size in a standard eye

      • Standard eye is defined as a +60.00D emmetrope

    • Axial ametrope

      • Hyperopia: eye is too short

      • Myopia: eye is too long

      • Axial ametropes best corrected with glasses: Knapp’s Law

        • Knapp’s Law: RSM is 1 in an ametrope if a thin lens is placed at the primary focal point of the eye

          • Primary focal point for axial ametrope is about 15-17 mm in front of cornea

          • Explains why glasses work better for axial ametropes (they correct for the length of the eye)

    • Refractive ametrope

      • Best corrected with contact lenses

      • Uncorrected refractive ametropes all have the same retinal image size whether they are hyperopic, myopic, or emmetropic (same length of the eye)

        • Need CLs to make sure the mag of the image remains constant even with optical correction for the refractive error

        • CLs have a small vertex distance (h) and thickness (t), so they don’t effect image magnification very much

Retinal Image Size

• Uncorrected axial ametropes

  • Retinal image size: myopes > emmetropes > hyperopes

    • Axial myopes have largest retinal image size (long eye)

• Corrected axial ametropes

  • Specs at the primary focal point of the eye give RSM = 1

  • CLs on axial ametropes don’t correct for retinal image size

• Uncorrected refractive ametropes

  • Hyperopes and myopes have the same retinal image size as emmetropes

• Corrected refractive ametropes

  • CLs don’t change the retinal image size, RSM = 1 in all refractive ametropes

  • Specs give a magnified retinal image size for hyperopes (+ lens) and minified retinal image size for myopes (- lens)

    • If one eye is +1.00 and one eye is -1.00, the +1.00 lens will have more SM (+ induces mag)

      • Make the (-) lens thicker and steeper or the (+) lens thinner and flatter to even out SM

• Aniseikonia: difference in size or shape of retinal images seen by left and right eyes (anatomical or induced)

  • Anatomical aniseikonia: difference in retinal images due to anatomical asymmetry, like discrepancy in photoreceptor density

  • Induced aniseikonia: difference in retinal images due to optics of vision correction, like differences in spectacle mag in Spec Rx

  • Overall aniseikonia: difference in image size between the two eyes effecting the entire field

  • Meridional aniseikonia: difference in image size between the two eyes due to difference in cylinder, causing the effect to be prominent in only one meridian

    • Can cause a straight line to look tilted

• Prescribing

  • Small differences in RSM: give equal BCs and equal thickness

  • Large differences in RSM: give the eye with the highest RSM a flatter, thinner lens

    • Increased BC and increased thickness increase RSM

    • Prescribe a thicker, steeper lens for the eye with the lower RSM

  • If one eye has a small Rx, and the other eye has an Rx over 4.00D, the ametropia is likely axial: prescribe specs

  • If one eye has a small Rx, and the other eye has an Rx under 4.00D, the ametropia is likely refractive: prescribe CLs

  • Aniseikonia from a large astigmatism is likely refractive/cornea-related: prescribe CLs

  • Every 1.00D power difference between the eyes gives 1% aniseikonia

• Anisometropia

  • Refractive state of the left eye is different to the refractive state of the right eye, usually by more than 1.00D

  • Accommodation occurs equally in both eyes

    • Myopic patients will use the more myopic eye for near vision (accommodate less) and the less myopic eye for distance vision (see better at distance)

      • Myopic patients don’t need to accommodate for distance, and might not need to accommodate too much for near, so accommodation should not effect them too much

    • Hyperopic anisometropic patients will likely not see clearly at any distance, because they need to accommodate even at distance

      • Hyperopic patients will use the least hyperopic eye to accommodate at all distances (needs to accommodate less, but still overworking)

      • Puts kids at risk for amblyopia at early childhood

      • Patients that are hyperopic can still have good DV by accommodating to bring the image forward, but they may have eyestrain from the constant need to accommodate

        • NV requires hyperopic patients to bring the image even further forward, and they might not be able to accommodate enough to do that

• Antimetropia: one eye is hyperopic and the other is myopic

Absorptive Lenses

• When light passes through a lens, it is reflected by both surfaces (front and back), and absorbed by the lens material

• Transmittance (t): measures the amount of light that gets through an optical system (0-1)

  • When light hits a lens it is lost in 2 ways: reflected at front and back surfaces, absorbed by lens material

    • To measure light reflected, use Fresnel’s law: reflection of light at the boundary between two media indices

      • R = (n₂-n₁/n₂+n₁)²

      • Use same number twice for front and back surface when looking for total transmittance (n₂ is lens medium)

    • To convert Fresnel’s law to transmittance:

      • T_s = 1-R

        • T_s: transmittance at each surface

        • Need to do this for front and back surface

    • To measure light absorbed, assume the amount transmitted by the medium is 1 - amount absorbed by the medium:

      • T_M = 1 - (amount of light absorbed by lens)

        • T_M: transmittance through media

  • To find total transmittance (T):

    • T = (T_S1)(T_S2)(T_M)

• Ideal thin film: choose film material that minimizes reflection

  • n_f = sqrt(n₁n_L)

    • n_f: index of film

    • n₁: index of initial medium (air)

    • n_L: index of lens

• Summary

  • Accommodation

    • Hyperopes accommodate less with CLs

      • Can need an add earlier

    • Myopes accommodate more with CLs

  • Magnification

    • Hyperopes have a smaller retinal image with CLs (less SM)

    • Myopes has a larger retinal image with CLs (less SM)

  • Vergence

    • Hyperopes converge less with CLs (less induced BO)

    • Myopes converge more with CLs (less induced BI)

    • CLs induce less prism

      • Prism in specs allows eyes to look in the direction with less work