Aberrations & Prism
Aberrations
Monochromatic Aberrations
Wavelength independent aberrations that distort image quality or deform image plane
Based on unpredictable behavior of large angle rays, combined with image distortion that is caused by positions of optical surfaces and limiting apertures
Spherical Aberration
Marginal rays (peripheral) focus in a different plane than paraxial rays (rays close to optic axis)
Only monochromatic aberration that impacts on-axis and off-axis rays*
Positive (undercorrected) SA: marginal rays focus in front of paraxial rays
Marginal rays are more (+) than paraxial rays
Occurs in positive surfaces
Negative (overcorrected) SA: marginal rays focus behind paraxial rays
Paraxial rays are more (+) than marginal rays
Negative surfaces or positive aspheric surfaces
Longitudinal SA: difference between marginal and paraxial ray foci along the optic axis
Difference in depth of focal points
Image becomes blurred
Contributes to nocturnal myopia
Lateral SA: difference in the position of marginal and paraxial ray positions in the plane of paraxial focus
Difference in vertical position in the plane of paraxial focus
Coma
In an off-axis point, marginal rays do not meet at the same place as paraxial rays laterally
Impacts only off-axis rays*
Causes varied magnification laterally
Results in an asymmetric, comet-shaped patch
Spherical aberrations and comas are not taken into consideration when designing lenses because only paraxial rays are able to pass through a small pupil size
However, if lenses are very high powered, aspheric lenses are necessary to compensate for spherical aberrations
Aspheric lens indications:
High powered lens: less than -23.00 D, more than +7.00 D
Flattening the lens or making it lighter
Progressives
Length of SA and coma increase with square root of pupil size (larger pupil size2 = longer aberration/worse image quality)
Area of SA and coma increase with cubed root of pupil size (larger pupil size3 = larger aberration/worse image quality)
Radial Astigmatism
Off-axis rays on spherical lenses hit the lens obliquely
3 types of off-axis rays that hit the retina at different angles: tangential, sagittal, petzval
Remember: teacup, saucer, plate
Causes flat object to yield an asymmetric/curved image
Can reduce RA by using a curved image surface (like move screen or retina)
Must be considered when designing lenses by picking the correct base curve to avoid RA
Tscherning Ellipse: BC vs. Fv plot that tells you what BC to choose for different lens powers to eliminate oblique astigmatism/RA
Made of 2 curves for a steeper or flatter BC
Wollaston Curve: steeper BC
Ostwalt Curve: flatter BC, more commonly used
Curves are limited under -22.00 D and over +7.50 D, when you need aspheric lenses to reduce RA
Curvature of field: without any RA, images would fall on a curved surface called the Petzval surface
Even with no RA, you would still have warpage of the image due to the curvature of the Petzval surface
To find curvature of field: K = F/n
K: curvature of image surface for a distance object
F: lens power
n: index of refraction of lens
Curvature of field is present anytime the Petzval surface is not equal to the far point sphere of the eye
Corrected curve lens: lens corrected for radial astigmatism, curvature of field, or both
Point focal lens: lens corrected for RA but not curvature of field
Percival form lens: lens corrected for curvature of field but not RA
Most lenses are made as a compromise of both so the lens is partially corrected for both RA and curvature of field
RA and curvature of field can both be reduced by choosing the correct BC and using a curved image surface
Distortion
Magnification of a point depends on the object distance from the optical axis
Straight line objects form straight line images only if the line passes through the optical axis
Minus lenses cause a barrel distortion
Plus lenses cause a pincushion distortion
In reality, distortion is most problematic for high powered lenses, like those used by aphakic patients
Chromatic Aberrations
Caused by the fact that refractive index (n) is wavelength dependent
Shorter wavelengths (blues, violets) bend more as they pass through an interface than longer wavelengths do
This makes the wavelengths focus in different locations, so a point object does not produce a point image
Abbe number (v) can be used to quantify chromatic aberration: Abbe value and chromatic aberration are inversely related
Longitudinal (axial) chromatic aberration: image varies in location
A point made of light from many wavelengths causes a series of point images to be projected along the visual axis
Inverse of Abbe value
CA = F/v
Lower Abbe value and higher F power = increased CA
Lateral (transverse) chromatic aberration: image varies in size
A point made of light from many wavelengths causes different size images to be projected depending on wavelength
Also causes different prismatic effects depending on wavelength
More prismatic effect = more harmful to vision
Inverse of Abbe value
CA = dF/v
d: distance from optical center
Lateral CA increases as we move towards lens periphery
Achromatic doublet: combining (+) lens of one material and (-) lens of another can eliminate chromatic aberrations
Total CA power (CA1+CA2) needs to equal 0
F1+F2 will equal the total power of the doublet
0 = F1/v1 + F2/v2
By balancing red-green during refraction, you are essentially balancing the chromatic aberrations to get a more precise refractive value
Low Abbe values (like in polycarb) will cause the most chromatic aberrations
To minimize CAs in lenses with low Abbe values:
Shorter vertex distance
Monocular PDs
Sufficient pantoscopic tilt
Prism
Deviation power: how far a light beam is diverted by a prism
Prism power = y/x
Y: linear distance prism will be shifted (cm)
X: distance between prism and wall (m)
Prism power: how far prism diverts light
Light is bent towards the base of the prism and image is bent towards the apex
Prism power & apex angle
For thin prisms and small incident angles, deviation angle can be found using:
d = A(n-1)
d: deviation angle (degrees)
Angle that light deviates from regular path due to prism
A: apex angle (degrees)
Angle of prism apex
This equation assumes that the prism lens is in air
Remember: dan-1 equation
Higher apex angle or higher index of refraction will result in a higher deviation angle
If the prism is in any material other than air:
Substitute ‘n’ for ‘np/ns’
Np: n of prism
Ns: n of surface
New formula becomes:
d = A((np/ns)-1)
1 degree of deviation angle = 1.75 prism diopters
Prism power & thickness
Prism power can be found using lens thickness:
Prism = 100 g(n-1)/l
g: difference in thickness between base and apex (base thickness-apex thickness)
l: length from apex to base
Prism effectivity
Depends on location of prism in relation to eye:
Prism effectivity = prism / (1-distance from prism to center of rotation/distance from prism to near object)
Prentice’s Rule
Each point on a lens has its own prism power, based on where it is in relation to the optic center
Each point on the lens bends light a certain amount
Prism = dF
Measuring prism power at a certain point on the lens
d: distance from the optic center (cm)
F: lens power
We can purposely induce prism by decentering a lens
For a plus lens, decenter in the direction of the base
If an Rx calls for BO, decenter the lens out
If the patient is looking down through the plus lens, the lens is made BU, so it is decentered upwards
For a minus lens, decenter in the direction of the apex
If an Rx calls for BO, decenter the lens in
If the patient is looking down through the minus lens, the lens is made BD, so it is decentered downwards
Prentice’s rule does not work on oblique astigmatisms
You can find a vertical or horizontal prism power in an oblique cylinder lens by finding the cylinder power in the horizontal or vertical axis
If x045 is -1.00 and x135 is -2.00, you know that the power at x090 is -1.50 D
Now you can use -1.50 as the F to find the prism in the vertical axis of that lens
Combining prisms
If 2 prisms are in the same direction (both vertical or both horizontal), they can be added or subtracted to get the power
If one prism is horizontal and one prism is vertical, use vector addition
Prism2 = H2 + V2
Prism Imbalance
If there is a different amount of vertical or horizontal prism in each eye, each eye experiences different prismatic effects, causing prism imbalance
Vertical prism imbalance
If both prisms are in the same direction, subtract
If the prisms are in opposite directions (BU and BD), add
Want to find the difference in the amount of prism in each eye
Horizontal prism imbalance
If both prism bases are the same, add
Technically, if both prisms are BO, they are pointing in opposite directions, but you would have to add them since they are the same
If the prism bases are opposite (BI and BO), subtract
Easier to think in terms of what direction the arrows are pointing (regardless of the base)
If the arrows are pointing in the same directions (both pointing up, both pointing right), subtract
If the arrows are pointing in opposite directions, add
For a prism imbalance equation, find prism in each eye with Prentice’s rule, and then add or subtract
Correcting vertical imbalance:
Slab off: make the more (-) lens more BU to compensate for the vertical imbalance
If you have one lens with a higher minus, making it more BU will counteract the high BD that it is inducing
If you have one lens with a lower plus, making it more BU will increase the BU effect to better match the other higher plus eye
If you need correction over 1.5 PD, the BU can get in the way of the line of sight
Dissimilar segs: since bifocals induce prismatic effect, placing segs at different locations will make different OCs and even out vertical imbalance
Multiple specs can be used instead of bifocals to be able to always look through the OC (one NV spec, one DV spec)
Contact lenses can be used so the OC moves with the eye
Fresnel prism: can act like a temporary slab off
Image Jump
Image displaces at bifocal line, making it look like it is jumping due to added prism in the seg
Prism comes from distance portion until eye crosses seg line, at which point prism comes from near portion
Calculating image jump: use Prentice’s rule with just the add power and the OC of the seg lens being used
Do not add the add power to the distance, and use just the add
Ex: If you have a flat top 28 with a +2.00D add, image jump is (2.00)(.5) = 1.00 PD BD of image jump
BD because switching into the top portion of a plus seg
Executive seg will not cause image jump because seg OC is 0
Total Prismatic Effect
Add the prism induced from looking away from the distance OC and prism induced from looking away from the seg OC
Calculate distance prism:
F: distance Rx in the 090 axis
Remember that if you are calculating vertical prism effect, you need to make sure the F is in the x090
d: total distance patient is looking away from the distance OC to read (in cm)
Cm patient is looking below the MRP to read
Calculate near prism:
F: just the near add power
d: distance patient is looking away from the seg OC to read (in cm)
Add the seg drop (distance between MRP and seg line) and the seg OC (based on type of seg being used) to get total distance between distance OC and seg OC
Subtract this from total distance patient is looking away from distance OC to read (in cm)
Ex: Patient is looking 15 mm below MRP to read, seg drop is 4 mm, and patient is wearing flat top 28
4mm(seg drop)+5mm(FT28 OC)=9mm
15mm(reading distance from MRP)-9mm=6mm(distance from seg OC to reading point)
Add the distance and near prism together
If distance lens is (+), both distance and near prism is BU (reading below the OC of a plus lens)