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Lenses

Near insets for ophthalmic lenses Part 2

31/10/2018
By Grant Hannaford
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In his previous contribution, GRANT HANNAFORD explored the topic of the derivations and purpose of facial measurements in optical dispensing. He continues his explanation here in part two of the series.

In the last article, we canvassed some of the various methods for determining inter pupillary distances (PD).

Here we continue this topic, beginning with an alternative method proposed by Daniel Gerstman (1973) that uses the intended working distance to determine inset. The rule states that for each dioptre of demand an inset of 0.75mm is applied.

It’s important note that the dioptric demand is used and not the add power. So for a common working distance of 40cm:


Similar to the methods employed by Clifford Brooks and Irvin Borish (2007), and Mo Jalie (2008) (covered in the previous article), the result again agrees reasonably well with the 2mm rule of thumb.

Note that these methods do not make compensation for the aberrations generated by the plane of the lens being oblique to the line of sight to the near point – this will be discussed in the future.

An interesting set of conditions arises for multifocal lenses (including bifocals), where the multiple zones require an inset for near vision (Jalie and Association of Dispensing Opticians [Great Britain] 2016). In these cases the impact of the distance powers must be considered, as they will generate an amount of prismatic effect.

For positive distance powers, the base out prism will cause the eye to over converge. Negative powers will cause the eye to under converge, due to the base in prism generated at the near point in the lens.

Vincent Ellerbrock (1948) developed an expression to account for the power of the distance lens when determining inset where again w is the working distance, d is the distance to centre of rotation and f is the focal length of the distance power lens:


The table below compares all of the methods described so far in this series for 400mm working distances.

If we consider a patient with a binocular PD of 60mm and a working distance of 400mm, the various methods for calculating near PD give us insets of 1.96mm (geometric), 1.8mm (Gerstman) and 1.76mm (Ellerbrock, plano distance power).

Table 4 gives a comparison of near PD results for the three methods outlined (Ellerbrock using a plano distance power).

As can be seen, these methods have a variance of approximately 0.1mm across the range of distance PDs shown, which in the context of most prescriptions is negligible.

To put this in the context of prismatic effect, using 0.25 dioptres of prism per eye as a boundary condition:


Clearly this exceeds a reasonable range of powers, so in the context of normal practice any of the methods described will give a reasonable result when calculating values for near PD.

While an argument may be made for using a rule of thumb value for calculating near insets and near PDs, the range of rules present in the industry are too wide for this to represent a reasonable technique.

The relative benefits in the methods described are left to the individual to decide on their preferred method.

In practice the generation of charts is a relatively trivial exercise and will allow the practitioner to ensure that best practice is being applied.

PDNear PDInsetPDNear PDInset
35.0032.712.2929.5027.571.93
34.5032.242.2629.0027.101.90
34.0031.782.228.5026.641.86
33.5031.312.1928.0026.171.83
33.0030.842.1627.5025.701.80
32.5030.372.1327.0025.231.77
32.0029.912.0926.5024.771.73
31.5029.442.0626.0024.301.70
31.0028.972.0325.5023.831.67
30.5028.502.0025.0023.361.64
30.0028.041.9624.5022.901.60
Table 1 - Geometric method for near centration (w=400mm)

 

Working distance (w) (cm)Dioptric Demand (D)Inset (mm)
205.003.75
303.332.50
402.501.88
502.001.50
601.671.25
701.431.07
801.250.94
901.110.83
1001.000.75
Table 2 - Gerstman method for near centration (w=400mm)

 

 Mono PD (mm)
Power(D)282930313233343536
5.001.871.932.002.072.132.202.272.332.40
4.001.821.881.952.012.082.142.212.272.34
3.001.771.841.901.962.032.092.152.222.28
2.001.731.791.851.911.982.042.102.162.22
1.001.691.751.811.871.931.992.052.112.17
0.001.651.711.761.821.881.942.002.062.12
-1.001.611.671.721.781.841.901.952.012.07
-2.001.571.631.691.741.801.851.911.972.02
-3.001.541.591.651.701.761.811.871.921.98
-4.001.511.561.611.671.721.771.831.881.94
-5.001.471.531.581.631.681.741.791.841.89
Table 3 - Ellerbrock method for inset (w=400mm)

 

w= 400mmw= 800mm
Dist PDGeometricGerstmanEllerbrockDist PDGeometricGerstmanEllerbrock
2826.1726.1326.352827.0527.0627.15
2927.1027.1327.292928.0228.0628.12
3028.0428.1328.243028.9929.0629.09
3128.9729.1329.183129.9530.0630.06
3229.9130.1330.123230.9231.0631.03
3330.8431.1331.063331.8832.0632.00
3431.7832.1332.003432.8533.0632.97
w= 600mmw= 1000mm
Dist PDGeometricGerstmanEllerbrockDist PDGeometricGerstmanEllerbrock
2826.7526.7526.882827.2427.2527.32
2927.7127.7527.842928.2128.2528.29
3028.6628.7528.803029.1829.2529.27
3129.6229.7529.763130.1630.2530.24
3230.5730.7530.723231.1331.2531.22
3331.5331.7531.683332.1032.2532.20
3432.4832.7532.643433.0733.2533.17
Table 4 - Comparison of Methods for Varying Working Distances

 






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