# Optical Forums > Ophthalmic Optics >  Diopters and Degrees

## OPTIDONN

OK I was reading in PRINCIPLES OF OPHTHALMIC LENSES something about converting diopters to degrees. How is this done and what is the relationship between the two? I am a little confused.

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## chip anderson

Only done in prism deviation.   One diopter deviates a point of light 1mm at a distance of one mm.   One degree (almost never used in eyewear, and when it is the precriber or optician usually doesn't know the difference or correct terminology) deviates light one degree on the 180 degree protractor scale.  This is usually only used in telescopes, astronomical calculations and long distance constructions.  Then one may actually have degrees, minites and seconds.


Chip:cheers:

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## CME4SPECS

> Only done in prism deviation.   One diopter deviates a point of light 1mm at a distance of one mm.   One degree (almost never used in eyewear, and when it is the precriber or optician usually doesn't know the difference or correct terminology) deviates light one degree on the 180 degree protractor scale.  This is usually only used in telescopes, astronomical calculations and long distance constructions.  Then one may actually have degrees, minites and seconds.
> 
> 
> Chip:cheers:


I always thought it was 1cm at 1m.

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## chip anderson

Specs, I think you are right.  Somewhere around here I have a book that describes the difference and how to calculate the variation from diopters to degrees.  


Chip

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## Darryl Meister

A prism diopter can be defined mathematically as:

*Prism = 100 * tan Angle*

where Angle is the angle of deviation in degrees. Solving for the angle of deviation gives us:

*Angle = arctan (Prism / 100)*

So, for instance, 1 prism diopter is equal to:

Angle = arctan (1 / 100) = 0.57 degrees

And 1 degree is equal to:

Prism = 100 * tan 1 = 1.75 prism diopters

For relatively small angles, since the tangent of an angle is nearly equal to the angle itself in radians, you can these as a rule-of-thumb:

*1 Prism Diopter for every 0.57 Degrees* and *1 Degree for every 1.75 Prism Diopters*

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## OPTIDONN

Ah! Thanks guys!!:cheers:

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## chip anderson

Once again Der Meister to da rescue.

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## QDO1

> I always thought it was 1cm at 1m.


that is correct.  This is a useful measure, as you can multiply it up and explain it to a patient easily - 7 prism dioptres relates to the image moving 7 cm @ 1 M or 70 cm @ 10M,  "Imagine a car headlight at 10M the light would be dispalces 70 cm - it would look like 2 cars etc...."

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## rolandclaur

hey optidonn, what is the exact name of that book and who wrote and published it and where can i get my hands on one?  Thanks

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## QDO1

> hey optidonn, what is the exact name of that book and who wrote and published it and where can i get my hands on one? Thanks


writen by Mo Jalie, ISBN: 0900099208 

It is an old but excelent book, and it still stretches me. Nowadays I wish it was updated to cover more modern lenses, but as the title says - its all about learning the PRINCIPLES

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## Darryl Meister

And your best bet is to order it directly from the Association of British Dispensing Opticians.

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## QDO1

Its worth keeping an eye on Ebay and Amazon (both of which dont have a copy at the moment)

I picked up my copy on Ebay for £4.00 !

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## HarryChiling

The diopter is a dirty unit of measure and before it had come around there was the degree and centrad.  The difference between the diopter and the centrad is that the diopter is how far the object is deviated perpendicular to the optical axis where the centrad is measured the same except it is measured on an arc wich is tangent to the diopter at the optical axis.  The both are very similar so in ophthalmic optics we chose to go with the diopter because of its simplicity.  The degree is also also a very accurate form of measure for a prism because the deviation stays the same when measuring in diopters or centrads, however when converting from diopters to degrees the inaccuracy of the diopter will follow you.

See Attachment

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## QDO1

> The diopter is a dirty unit of measure and before it had come around there was the degree and centrad. The difference between the diopter and the centrad is that the diopter is how far the object is deviated perpendicular to the optical axis where the centrad is measured the same except it is measured on an arc wich is tangent to the diopter at the optical axis. The both are very similar so in ophthalmic optics we chose to go with the diopter because of its simplicity. The degree is also also a very accurate form of measure for a prism because the deviation stays the same when measuring in diopters or centrads, however when converting from diopters to degrees the inaccuracy of the diopter will follow you.
> 
> See Attachment


surley the dioptre and degree are interchangable, the  dioptre being just the angle expressed as 2 sides of a triangle, one of the sides being fixed at 1M.  or, are you saying that the formula we use to convert to a angle is throwing the accuracy away?

here lies the difference: I think between what we do in practice - measure a patients prisim against another prism of the same value untill the exibited diplopia is nutralised, and then we check the prism as a image displacment in a focimiter... which compares to the way a lens designer, or surfacer sees prism - as an angle

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## Darryl Meister

> surley the dioptre and degree are interchangable, the dioptre being just the angle expressed as 2 sides of a triangle, one of the sides being fixed at 1M. or, are you saying that the formula we use to convert to a angle is throwing the accuracy away?


The formula I provided above will allow you to interchange between the two measurements, and the approximation (1 degree = 1.75 prism diopters) will be very close for the angles you're likely to see in ophthalmics. The problem is that the tangent of an angle increases more rapidly than the angle itself. Consequently, since the prism diopter is based on the _tangent_ of an angle (100 * tan Angle), it is really a non-linear unit of measurement.

For instance, 1 degree of deviation is:

Prism = 100 * tan (1 deg)
Prism = 1.75 prism diopters

While 40 degrees of deviation is:

Prism 100 * tan (40 deg)
Prism = 83.91 prism diopters

Note that 83.91 / 1.75 = 48. If the _prism diopter_ were a true, (linear) unit of measurement like the _degree_, 40 degrees of deviation _should_ equal 1.75 * 40 = 70 prism diopters. However, because the tangent increases in a non-linear way, it actually equals 84 prism diopters.

However, this is only becomes a problem for large angles (above 30-35 prism diopters). For the prismatic measurements used in practice, the prism diopter is "close enough," and is very nearly proportional to the degree. It's also much _easier_ to use the prism diopter in practice, since you can measure the deviation on a flat plane. (Measuring centrads or degrees would require a curved measurement plane.)

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## QDO1

perhaps my reply was a bit lacking in detail.  I understand the relationship between prism dioptre and degrees - it just strikes me that it suits the ophthalmic practice to work in prism dioptres, but lens designers or surfacers to work in degrees

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## Darryl Meister

> it just strikes me that it suits the ophthalmic practice to work in prism dioptres, but lens designers or surfacers to work in degrees


I think we pretty much all work in prism diopters.

If you're working with a conventional generator, you may use prism rings or wedges, and some lab techs may unknowingly refer to the labeled numbers on these rings as "degrees." However, as far as I know these are all actually labeled in prism diopters. While surfacing software might convert back and forth between the two, the only time the _user_ sees or works with degrees is when the rectangular (base up/down, in/out) prism measurements from the refractionist have been converted into polar (@ axis) measurements for surfacing purposes.

Our lens designers also work in prism diopters, since it's easier to evaluate the results in the terms of visual and optical standards.

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## QDO1

facinating - the maths head on me says - convert to degrees ASAP cos the tangent thing is out of the way. The logical head says - we generally deal with less than 30 PD per eye, and PD is dead handy in practice so keep using it, and on the other surfacing software (using more than one index) must dive straight into a degrees measurement

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## Darryl Meister

Keep in mind that, since both doctors and dispensers measure prism in prism diopters, which will certainly be the case for the foreseeable future, the mathematical subtleties invovled won't matter -- and are generally handled by computer software nowadays, anyway. It just becomes an interesting conversation topic for the Ophthalmic Optics forum. ;)

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## shanbaum

> If you're working with a conventional generator, you may use prism rings or wedges, and some lab techs may unknowingly refer to the labeled numbers on these rings as "degrees." However, as far as I know these are all actually labeled in prism diopters. While surfacing software might convert back and forth between the two, the only time the _user_ sees or works with degrees is when the rectangular (base up/down, in/out) prism measurements from the refractionist have been converted into polar (@ axis) measurements for surfacing purposes.


Until recently, the prism rings used on Loh prism blockers were invariably marked in degrees.

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## Darryl Meister

> Until recently, the prism rings used on Loh prism blockers were invariably marked in degrees.


Good point, particularly for QDO and anyone else "across the pond," though I don't know that Loh prism blockers were ever very common over here (at least in the days prior to CNC surfacing)...?

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## HarryChiling

The only reason why I would even know anything about the centrad is the fact that I work with a pediatric ophthalmologist and the topic has come up due to strabismus and the fact that we commonly use high prisms (10-25 diopters, fresnal).  The centrad has come up as a topic of conversation.   I have never seen anyone use it and it makes for a great problem when you are trying to fool someone.

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## QDO1

> Good point, particularly for QDO and anyone else "across the pond," though I don't know that Loh prism blockers were ever very common over here (at least in the days prior to CNC surfacing)...?


I surfaced pre-CNC, so I know all about Prism rings - all fun stuff

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## shanbaum

> Good point, particularly for QDO and anyone else "across the pond," though I don't know that Loh prism blockers were ever very common over here (at least in the days prior to CNC surfacing)...?


They were only as common as Loh systems generally, which is to say, "not very".  A few labs used the Autoflow (now Norville) prism blocker, but those were even more rare.

As far as prism blocking in general is concerned, however, it's not obsolete; I understand that the Loh and Schneider cut-to-polish systems both require it.  Cutting prism at the generator places makes the task of producing a polishable surface significantly more difficult.

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