Chromatic Aberrations

Lens aberrations

In traditional geometrical optics, we assumed that any point on a lens produces an image which is a precise point-by-point copy of object at least in terms of shape, if not size in a position defined by simple formulae. This is not the case because formulae use small-angle approximation b = sin b = tan b these are therefore paraxial  (“close to the axis”) formulae, refractive index varies with wavelength - dispersion. Aberrations are the result. Monochromatic aberrations - spherical aberration, coma, oblique astigmatism, (field) curvature, distortion. Chromatic aberration - axial (longitudinal), transverse. Consider separately, although in reality, all happen simultaneously to a variable extent.

Why does it matter

For patients - Everyday devices are sold based on image quality, Smartphone cameras and screen; HD TV. The lens may not perform as expected - May not see as well as with trial case lenses in trial frame, Image quality not the same in all parts of the lens. For practitioner - Need to use this to help with lens choices, Need to be able to guide patient expectations.

What does Chromatic Aberration Look Like

View the illuminated Snellen chart. Monocularly. Through a 20∆ prism (use a prism bar). You should see coloured fringes in the direction of the base apex line. Hold the prism with base left. Left edge of chart will seem to have a red/yellow border. Right edge of chart will have a blue border. Turn the prism so base is down and the colours disappear from the sides of the chart.

Chromatic Aberration

lens refractive index quoted is n_d. refractive index for helium d-line wavelength = 587.6nm. n_F   wl  = 486.1nm hydrogen F-line

n_c    wl = 656.3nm  hydrogen c-line

dispersion = n_F - n_c

                     n_d - 1

constringence (V-value, Abbe number)

     =       1___         

       dispersion

Typical Parameters

Crown Glass: nc = 1.5204, nd = 1.5230, nf = 1.5293, V = 58.6.

Dense Flint: nc = 1.6602, nd = 1.6660, nf = 1.6807, V = 32.4

Axial or Longitudinal

if n greater, then deviation (power) greater for that wl. axial chromatic aberration (ACA) is dioptric distance between F_F’ and F_c’. (Duochrome test uses ACA/LCA of the eye).

in general F = (n-1) ( 1  -  1 )

                                   r₁    r₂

or more precisely  F_d = (n_d-1) ( 1  -  1 )

                                                  r₁    r₂

so  ( 1  -  1 )   =    F_d   

         r₁    r₂          (n_d-1)

ACA = F_F - F_c

 F_F = (n_F-1) ( 1  -  1 )  = (n_F-1)   F_d

                      r₁    r₂           (n_d-1)

 F_c = (n_c-1) ( 1  -  1 )  = (n_c-1)    F_d

                      r₁    r₂            (n_d-1)

ACA = (n_F-1)  F_d     -      (n_c-1)  F_d

            (n_d-1)              (n_d-1)

         = (n_F-1 - n_c - (-1))  F_d   =    (n_F-n_c)  F_d  =  F_d

             (n_d-1)                        (n_d-1)         V 

ACA

increases as lens power increases. decreases as constringence increases. eg: CR39 V = 58   F_d = +10.00DS. ACA = F_d/V = 10/58 = 0.17DS, the lens is 0.17DS stronger for blue than for red light, regardless of vergence. Less than ACA of the eye (compare to duochrome). Does it create inaccuracy on focimetry? 

Transverse Chromatic Aberration

the effect of chromatic aberration on vision away from optical centre of lens. TCA is difference in deviation for blue and red light. TCA = prismatic effect for blue - prismatic effect for red.

TCA = yF_F - yF_c  =  y(F_F - F_c)    (y in cms)

but ACA = (F_F - F_c) = F_d    so TCA = yF_d

                                   V                    V

                                                          = prismatic effect

                                                             constringence

can include sign of lens power and decentration in formula. final answer gives positive or negative TCA . refers to base direction of prismatic deviation. usually easiest to use that instead.

Calculations

TCA = prismatic effect

            constringence

TCA = yF_d

            V         

CR39: -10.00DS y = 5mm  V = 58

TCA = yF_d/V = 0.5 x 10/58 = 0.08D

Polycarbonate: -10.00DS y = 5mm V = 30

TCA = yF_d/V = 0.5 x 10/30 = 0.17D

When is TCA a problem for patients

It is usually assumed that 0.1D is the minimum noticeable amount. Where on a lens will have this amount of TCA?

TCA = yF_d/V  so yF_d = TCA x V

For CR39 yFd = 0.1 x 58 = 5.8D

patient may notice it anywhere on lens with 5.8D or more prismatic effect

For polycarbonate yFd = 0.1 x 30 = 3D

patient may notice it anywhere on lens with 3D  or more prismatic effect

Shortcut – critical ∆ = V/10

Influences choice of material.

Will TCA be noticeable?

Trivex - RE +1.00  LE +1.00. V = 45; critical value of prism = 4.5∆; where on lens? c = P/F = 4.5/1 = 4.5cms from the OC. No problem

1.74 plastic RE -6.00  LE -6.00. V = 33; critical value of prism = 3.3∆; where on lens? c = P/F = 3.3/6  = 0.55cms from the OC. Could be noticeable in normal lens usage.

Subjective Awareness of TCA

A bright white object creates a white image with a red fringe closest to prism base, and a blue fringe furthest from prism base. If object low contrast the colour is not noticed and edge just seems blurry.

Practical Consequences

no TCA at optical centre. may influence choice of lens material if good vision required through edge of lens. consider not using low V material if patient has prescribed prism. Eg RE -1.00  LE -1.00    4∆ base UP RE. Split prism between the eyes (also equalises lens thickness and weight). consider specifying vertical as well as horizontal centration in low V lenses. usually just specify horizontal centration by setting OCD = PD. This could make lenses much thicker in some places.

Optical Centration in Bifocals

ALL except Franklin spilt behave as if the segment is a separate small lens superimposed on a full size distance lens. Even if DOC at DVP, then at NVP, there will be H and V prism from main lens and V prism from segment. And can be H prism at NVP if seg centre not in line with NVP. P = c x F. P_VR = 1 x 4 = 4D UP. P_VL = 1 x 4 = 4D UP. Diff V prism = zero. No effect on binocular vision. Prism at NVP is not the same as Jump - The amount of jump is equal to prismatic effect of edge of segment. P = r x Add. For downcurve/round segment, r = radius of segment in cm. The base UP from the main lens in near vision would be REDUCED by choosing a downcurve/round segment but INCREASED by selecting a flat-top segment.

Reducing Vertical Prism at NVP

In contrast, a flat-top segment would be better to neutralise vertical prism at near if distance Rx is MINUS. any prismatic effect will be accompanied by TCA, will result in poor image quality for near vision, Can we calculate how much? To keep it simple, we will only consider vertical prism, we will compare D-seg and round segments, do we get expected difference in + and - lenses? Consider the lens as two separate components - F is distance, A is segment (addition) - even though really a single lens. TCA due to distance lens = yF/V. TCA due to segment = y_sA/V. TCA = (y_sA + yF)/V.

Comments

Highlighted values are those which might be expected to cause problems. TCA>0.1D. TCA contributed by the segment is minimal. Most of TCA is contributed by the main lens. With +/- 1.00 distance Rx, none of values reach the threshold. But around 5-10mm below seg top (near NVP) the findings are as predicted. Larger amounts of TCA in any design in lower part of segment (but rarely used?).

Segment Shape Choices

TCA will be minimal in low-moderate plus or minus prescriptions. TCA would not preclude using flat-top for plus, or downcurve for minus prescriptions. Flat-top would have less jump. Downcurve would be better cosmetically - knife-edge thickness.

TCA in Varifocals

Fitting cross isn’t at prism reference point. Cosmetic thinning prism included. ?may reduce distance acuity in high Rx/high index lenses. Consider V value more carefully for PAL(and bifocal) than for SV lenses.

Summary

We have considered chromatic aberration. Based on prismatic effect and V value (constringence). Once material is chosen, there is very little that can be done about it. It will be more noticeable in multifocal/PAL compared to single vision. Warn a px who is new to these lenses even if had high-index before. All the other aberrations are monochromatic. Occur even if only a single wavelength of light. They will depend on lens form, and only very slightly on material.