The Boddy Formula
For plus and minus digital progressive lenses
A new formula to replace Vogel’s rule
Brian Boddy
1/25/2013
The Boddy Formula
Base curves for minus digital lenses:
4.25 + ((Spherical equivalent + add)/2)
Base curves for plus digital lenses:
3.50 + ((add power/2) + Spherical equivalent)
The Boddy base curve formula for plus and minus digital progressive lenses:
Imagine offering your customers and patients every semi-finished single vision lens in every
color option available in the world today as a progressive lens in almost every frame. Until a few
years ago we, in the laboratory, kept the lens book right next to the layout computer. Daily, we
had to call back our wholesale account and tell them that the requested progressive was not
available in the material or color they sold to the patient.
Being one of the first retail stores to surface and brand private label progressives, we enjoyed a
freedom to sell almost any lens material in any lens option using backside progressive or
freeform technology. Unfortunately many times we outpaced our LMS (Laboratory Management
System) system due to the sheer volume of lenses and digital progressives that required updating.
On one occasion a dispenser sold a progressive in violet polarized plastic that needed to be done
in a day! With little demand for such a unique almost one of a kind lens it became necessary to
create a formula for my lab personnel to follow when filling these truly unique and very custom
backside digital progressive lens orders. This formula is called The Boddy Formula, for Plus
and Minus digital progressive lenses.
Disclaimer:
The Boddy Formula should never be used to replace the well researched and founded digital lens designers and
manufacturers base curve selection for legacy products. This research has designed very complex formulas to
arrive at the most optically correct curve for their back side digital progressive designs.
The Boddy formula was created to offer a mathematically derived base curve from sound optical principles for
use by opticians and para-optometrics in the following circumstances.

The LMS is down

The correct base curve for a lens has to be ordered prior to being input into the LMS

The layout program has a problem arriving at a base curve.
Often in the real world the available progressive lens option is not setup or available in the LMS and the
laboratory has found it necessary to pull the closest to correct base curve for the prescription and apply the
progressive to that lens. This is why I designed a universal formula to standardize the digital base curve selection
process.
In discussion with outside laboratories, I am told that they provide flatter and flatter base curves
for digital backside progressive plus lenses because of demands by an increasing number of
opticians who want thinner and thinner lenses. While I must concede changing the base curve
was marginally acceptable and it “somewhat” worked in the past (despite the manufacturers
warnings) with front side molded progressives aspheric and digital technologies for the near or
distance reference point corrupt the lens designers intent for the correction of aberrations or lens
errors. This however will not work with backside progressives and I suggest using The Boddy
Formula, for digital backside progressives. Making digital backside progressives flatter by
changing the base curves outside the manufacturer’s recommendations increases the possibility
of creating bi-convex lenses and/or lenses that will perform poorly. For example:
Prescription:
OD +2.25 sphere 3.00 add
OS +2.25 sphere 3.00 add
Most laboratories would place the above prescription on a 4.25 base front and backside
progressives in most materials. This would not work with back side progressives because it
creates a bi-convex ocular (backside curve).While the back curve at the DRP (distance reference
point) is around -2.00 D and is within the manufactures threshold, the curve at the NRP (near
reference point) would be a convex +0.75. For simplicity and ease of discussion this does not
consider prism thinning, index of refraction or sagittal value.
The results of a too flat base curve flatter is poor optics and is often unseen or over looked in the
making of digital plus lenses. Flatter base curves are very common in today’s market and at first
glance seems to satisfy the retail dispensers and customer wishes for flatter seemingly more
cosmetically appealing lenses. Let’s pause for a moment and look back at why we use specific
front side or base curves: First the definition:
BASE CURVE
A manufacturer – marked (or nominal) surface power for the first side curve to be ground and
polished on a series of finished or semi – finished corrected or uncorrected lenses, which, when
combined with the second side ground and polished curvature, produces the desired lens power.
Base curves, for a given range of powers, can be of a common marked value, either plus or
minus, spherical or toric (i.e., cylindrical) in configuration depending on the correction(s) for
which the series of lenses were designed.(from Dictionary of Ophthalmic Optics Opticianry,
1995) (Opticianry, 1995)
The front curve is our starting curve and every calculation made includes that front surface
because of original research by Dr Tscherning and is represented as an ellipse.
Tscherning’s Ellipse
From the Dictionary of Ophthalmic Optics, 1995, “Marcus Hans Eric Tscherning (chern’ings)
curve/ellipse or corrected curve theory (Tscherning’s curve: A nomogram displaying on an
elliptically plotted curved line the optimal front curvature of an ophthalmic lens for its dioptric
power to minimize oblique astigmatic aberration; the basis for so-called corrected curve lenses
(Orthogon, Tillyer, etc.) Developed in 1904 by Marcus Hans Eric Tscherning (1854-1939),
ophthalmologist of Paris and Copenhagen; Tscherning’s ellipse.” (Opticianry, 1995)
Darryl Meister’s Opthalmic Lens Design 20/20 Magazine May 1st 2010 (ABOM, 2010)
I am very sure that in 1904 when Dr Tscherning created this ellipse the public at large was
basically happy to see that the opticians of the day had firm guidelines for which to select base
curves. Today’s customers and patients want to see clearly through the entire area of their
spectacle lenses, from edge to edge, as if looking through the optical center. They could care less
about the constraints of physics and the limitations of our optical laboratories. The eye that
turned behind 10 year old optics or the now archaic term of “conventional spectacle lenses”saw
off axis (off center) and that was affected by aberrations and elliptical errors that were not always
corrected by the fining and polishing process. Conventional lenses, using Tscherning’s ellipse
could minimize these aberrations (specifically marginal astigmatism) by using the correct base
curve also called best form or corrected curve lens design i.e.,the best base or front curve for the
best overall management of off axis aberrations.
Irwin Vogel, an Opticianry instructor from New York City Community College and later at
Cañada College in Redwood City CA created a formula to simplify Tscherning’s work. Vogel’s
Rule is: (Underwood, 2008)
Plus lenses: Front base curve = spherical equivalent + 6.00
Minus lenses: front base curve = ½ spherical equivalent + 6.00
This simple formula has been an effective guide for specifying base curve using best form
principles. (Advanced Opticians Tutorial page 97-98)
To affirm our adherence to these foundational principals we receive written directions on the
patient’s prescriptions from the Doctor stating: “use habitual base curve”. This has its
foundation in keeping the magnification effects the same to avoid the patient’s comments about
difficulty “getting used to” their new glasses. However, it compromises the changes that modern
technologies provide in new lenses. Labs that provide digital lenses change the base curves
because digital lens algorithms are guiding the calculations. These calculations theoretically
compensate any number of image errors and the best form is theoretically calculated and
corrected to compensate for any base curve the lab chooses on which to put the prescription. In
spite of the manufactures and Dr’s recommendations is it now okay in the digital lens age to
throw traditional base curves out and succumb to the retail dispenser and consumers wishes? If
we replace Vogel’s Rule with The Boddy Formula lenses can be produced mathematically
correct on a middle ground i.e., thinner, flatter lenses, without comprising optics.
Currently if we apply Vogel’s rule to back side progressives we don’t have the ability to
calculate at what point that front curve is too steep or too flat and this results in bi-convex and/or
too flat or, other lenses that perform poorly. With digitally compensated lenses we have the
freedom to cut lenses flatter and, to some degree not sacrifice optics by compensating for the
changes in base curve. However we should not guess at the best base curve that ultimately
becomes too flat or worse crosses the bi-convex threshold. A standardized formula to arrive at
the best base curve for the job, that meets all parties’ expectations, is needed. In addition, few
manufactures are printing and providing base curve charts that were readily available in the past
making the task of pulling the correct base curve more difficult.
Therefore, The Boddy Formula factors in the spherical equivalent power and the add power to
derive the best base curve for a digital backside progressive, both at DRP and NRP. Applying
The Boddy Formula gives everyone what they are looking for, thinner lenses that perform better
and manufactures get lenses that do not fall below a -2.00 D ocular curve.
THE BODDY FORMULA
For minus digital lenses:
4.25 + ((Spherical equivalent + add)/2)
I replaced Vogel’s Rule of thumb ocular curve from the 6.00 diopters to 4.25 because the 4.25 diopter
number more accurately represents the aspheric mean of a plano lens when placed on a 4.25 diopter base
curve. Digital lenses are designed aspheric for spherical Rx’s and atoric for cylindrical Rx’s on the
backside of the lens.
For plus digital lenses is:
3.50 + ((add power/2) + Spherical equivalent)
In plus prescriptions I used 3.50 diopters as the rule for two reasons. The first is addressed
above; the lens will be aspheric and/or atoric on the backside. The second reason is, unlike
Vogel’s Rule, by incorporating the add power into the base curve equation assures that the
resulting base curve choice will not be too flat or become bi-convex so the result is the best
optically performing lens.
Let’s look at the prescription above and apply the Boddy Formula to it:
OD +2.25 sphere 3.00 add
OS +2.25 sphere 3.00 add
The Boddy Formula calculation would be: 3.50 + ((add power/2) + Spherical equivalent)
= 3.50 + ((3.00/2) + 2.25)
= 3.50 + (3.75)
= 7.25 D
Applying my formula suggests using a 7.25 D base curve. While this a diopter less than Vogel’s
Rule suggestion of 8.25 diopter base curve it is above the 6.00 diopter base curve most
laboratories would grind this prescription on. Why would I suggest a higher base curve?
Here is why my formula works. At the NRP the resulting ocular curve would be -2.00, which is
an optimal aspheric backside curve,. If we used a 6.00 diopter base curve lens the resulting curve
at NRP would be -1.00, below the manufacturer recommended threshold for quality aspheric
lenses.
Below is a picture copy of the Excel spreadsheet that I created to validate and test my formula.
Note on the very left column is the Sphere power with the add power located next to it with a
side by side comparison of my formula and Vogel’s Rule.
Now let’s look at the same prescription but change the add power:
OD +2.25 sphere 2.00 add
OS +2.25 sphere 2.00 add
The Boddy Formula calculation would be: 3.50 + ((add power/2) + Spherical equivalent)
= 3.50 + ((2.00/2) + 2.25)
=3.50 + (3.25)
= 6.75 D
Applying my formula with a new add power now suggests using a 6.75 D base curve which is
1.50 D less than Vogel’s Rule and 0.50 D less than the 3.00 add we calculated before. The new
base curve results in an ocular NRP curve of -2.50. Including the add power in the base curve
decision making results in a more uniform backside or ocular curve delivering far better optics
and more uniform vision in digital progressives.
Below is a picture showing the changes to a 2.00 add:
CONCLUSION
Quit sacrificing cosmetics for optics! Being a second generation optician my father said it, I say
it and every lab man and women in the country continue to mutter these words and now I tell my
kids the same thing. Quit sacrificing cosmetics for optics!
If we all say it, why is the retail optician still asking us for flatter base curves and equating that to
thinner lenses and even worse labs delivering these comprised lenses! “Aspheric's!” declared the
optician to my lab manager “You made these lenses thinner the last time by using that new
aspheric technology and not only did you make it thinner you made the base curve flatter! Now I
want these progressive lenses made with a flatter base curve using that aspheric technology!”
I want everyone to understand that with backside digital progressive optics the base curve change
is necessary to facilitate the accommodation of the progressive being placed on the backside of
the lens. Most opticians and consumers will not notice the change and I hope the ones that do
will have read this paper and understand why this has come about. Let’s face it, we all want to
offer superior lenses from our laboratory, store or office and to that end we all add or take away
something from the process that makes us unique, better or differentiates us from our
competition. But, let’s not do it in such a way that comprises our integrity. I propose we make
changes in other ways but stick very closely to a universally agreed upon base curve. The agreed
upon formula can no longer be static like our well founded Vogel’s Rule but now with our new
found freedoms in digital and major advances in computers and digital processing we can do
away with the old formulas and incorporate more robust formulas that address today’s needs.
The Boddy formula addresses the new and emerging digital lens technologies but is dynamic to
incorporate unknown future optical technologies while incorporating the add power into the
equation. We can now deliver better optics to the consumer using contemporary formulas.
Establishing an industry wide agreed upon formula gives the consumer the best possible optics
with lenses that are lighter and thinner.
Brian Boddy
Post Office Box 6079
Santa Fe NM 87502
505-471-2020 office
505-670-7501 cell
Brian@AcomaOptical.com
BrianBoddy@ymail.com
ATTACHMENT
Excel base curve charts created for plus and minus lenses with a screen shot of the free Excel file
available to any optical lab that requests it.
Biblography
ABOM Darryl Meister Technical Marketing Manager Carl Zeiss Vision [Online] //
www.2020mag.com. - May 1, 2010. http://www.2020mag.com/ce/TTViewTest.aspx?LessonId=106734.
Opticianry Arthur H Keeney Robert E. Hagman Cosmo J Fratello and The National
Academy of Dictionary of Ophthalmic Optics [Book]. - Woburn : Butterworth - Heinemann,
1995.
Underwood Michael R DiSanto Diane F. Drake Randall L Smith William B Advanced
Opticians Tutorial [Book]. - Landover : [s.n.], 2008.