Distortion Curves for Various Eyepieces.


Copyright – P. J. Smith


I have placed this material on my web site to enable more informed discussion on distortion characteristics of various eyepieces.

I must point out that one should be very wary about condemning an eyepiece on its distortion characteristics.  An eyepiece is a compromise between complexity, sharpness, apparent field of view, eyerelief, field curvature, and distortion.

Distortion is low on my list except for a few special cases.  With small or even moderate apparent fields of view it is usually of no consequence and almost ‘invisible’.  The advent of the ‘superwides’ has brought the subject into prominence with some people quite vocal on preferences.

In most cases, information has been taken from patent literature.  Since the US Patent material is most accessible, I have used this and will give references.  In a few cases, some examples have been taken from Japanese Patents and the US MIL handbook of Optical Design because this refers to them as good, typical, examples.  Thus, all of this information should be traceable for a serious researcher.  It is of interest that this handbook, which is now quite old, implied eyepiece design had matured to such an extent that there was little to be gained spending much time on more advanced eyepiece design.  Whoever authored that probably now regrets the statement!


In no cases should this information be used to malign some eyepiece

 without a full study of all other aberrations. 


This is only one aspect of performance and in my opinion

other factors are far more important.



 To aid in making comparisons, I have arranged all plots to the same scale.  In some cases, this has caused certain extreme wide field examples to produce plots off scale.

The range of the plots has also been standardised as much as possible.  In the case of the moderate field examples, a 60 degree (30 degree semi-field) has been used for all plots.  This is often more than what the eyepiece can stand in terms of sharpness and astigmatism.  Realistic fields will be given and you will have to apply this to the graphs in some cases. 

The reason this has been done is to allow a more valid comparison between the distortion figures of different types of eyepiece constructions. 

It should also be pointed out that the choice of different glasses can have a major effect on distortion so one should not assume all eyepieces which look to have a similar structure have the same distortion characteristics.  It is tempting to classify all eyepieces by element/group construction.  While this is something I use a lot for naming eyepiece files, it is more for the convenience of locating specific files among the plethora of eyepieces I have on file rather than being a good predictor of performance.

Extreme field eyepieces may have different fields.  These will be given.  Be careful when comparing superwides with other eyepieces.  Although the extreme field distortion figure is of interest, any fair comparison should only be made out to the same apparent field of view.


All output is from Zemax and I have arranged superimposed plots of distortion based on two criteria.


Distortion is measured by considering the departure from various ideal criteria.

F Tan(θ) curves are what is usually called ‘Standard’ distortion.

F (θ) curves are related to angular distortion.

In some cases, especially where eyepieces have been originally designed for instruments with very short focal length objectives, the eyerelief figures originally given are inappropriate when used in longer telescopes.  For this reason, for assessment purposes, I have often modified material in patent literature in this respect.  This reflects what would happen if a person took measurements of these eyepieces with astronomical telescopes.

The actual eyepiece prescriptions have NOT been changed.


Distortion curves are not changed much by doing this.





Albert Koenig.  USPat. 2217281.   Filed 1938   Afv = 50°

One of many designs for Carl Zeiss.

50° of the 60° plot is used.


Mil Hdbk   Afv = 50°

40° of the 60° plot is used.


These are examples of what, today, is usually called the ‘Orthoscopic’ or Abbe configuration.  It should be noted that over the years, the word ‘Orthoscopic’ has been used in conjunction with other types.  Most assume that any ‘Orthoscopic’ type has almost zero Rectilinear distortion.




Albert Koenig.  USPat. 2217281.   Filed 1938   Afv = 50°

One of many designs for Carl Zeiss.

50° of the 60° plot is used.


This is an unsymmetric design and as such is somewhat different from the common ‘Ploessl’ as sold today.



Mil Hdbk   Afv = 50°

50° of the 60° plot is used.


Albert Nagler USPat. 4482217.  Filed 1983.   Afv = 50°

50° of the 60° plot is used.

Because it is so common, yet made to high standards, this has been included.  Definition is better in this example of a ‘Ploessl’ than many others.  It is also better than some other ‘Ploessl’s’  for ghosting because the refractive index of both glass types is almost the same.



Satoshi Fukumoto USPat. 5546237.  Filed 1994.   Afv = 56°

56° of the 60° plot is used.

While not all eyepieces using aspheric surfaces have distortion characteristics similar to this one, it shows how the extra freedom of aspheric surfaces may be used to tailor the distortion curves as one wishes. 


It is also possible to produce this type of distortion characteristic with all spherical surfaces although it is very uncommon.  The two eyepieces below from Japanese Patents are examples.

Japanese Patent 07-063996.  Filed 1993.   Afv = 56°

56° of the 60° plot is used.



Japanese Patent 07-281108.  Filed 1994.   Afv = 60°

60° of the 60° plot is used.




Heinrich Erfle.  USPat. 1478704.   Filed 1921   Afv = 65°

One of many designs for Carl Zeiss.

65° of the 80° plot is used.  This was the first really wide field eyepiece. 



Christian von Hofe ( Goerz) USPat. 1759529.  Filed 1924   Afv = 75°

75° of the 80° plot is used.



Ludwig Jacob Bertele.  USPat. 1699682.   Filed 1925   Afv = 70°

70° of the 80° plot is used.




Albert Koenig.  USPat. 2206195.   Filed 1938   Afv = 70°

One of many designs for Carl Zeiss

70° of the 80° plot is used.



Ludwig Jacob Bertele.  (designed for Wild, Herbrugg), USPat. 2549158.   Filed 1947   Afv = 80°

80° of the 80° plot is used.



Ludwig Jacob Bertele.  (designed for Wild, Herrbrugg), USPat. 2549158.   Filed 1947   Afv = 80°

80° of the 80° plot is used.



Albert Nagler USPat. 4525035.  Filed 1984.   Afv = 70°

70° of the 80° plot is used.



Albert Nagler USPat. 4286844.  Filed 1979.   Afv = 80°

This is the original ‘Nagler’ eyepiece known to many.  It was not the first eyepiece to cover such huge fields, nor is it the first to use this general layout.  It was, however, the first readily available eyepiece of its type to be made available to ATM’s with excellent definition extending far off axis.  Many other superwide eyepieces before it were for military use where definition near the edge is considered less important than an extremely wide field.



Yasunori Ueno Nagler USPat. 5638213.  Filed 1995.   Afv = 80°

One of many of his designs for Nikon.


Many other designs of this type exist although it would appear that many have not been manufactured.  Some are less extreme.


These two have been chosen to illustrate that the distortion characteristics can be tailored to suite demands to some extent.  In both cases, the afov is designed for, and plotted for, 80°.



It is possible to exercise more control over distortion with the extra freedom introduced by using aspheric surfaces.  Of course not all aspheric eyepieces are of this distortion type.

Another example using aspherics has been included under Moderate field types.


Robert Richter USPat. 1968222.  Filed 1933.   Afv = 65°

The eyepiece was only intended to cover about 65° of the 80° plot used here.

 65° was quite a wide field back in 1933.



Jean Cojan.  USPat. 2528468.   Filed 1950   Afv = 80°

One of many of his designs, all with a parabolic surface.  The plot covers 80°.


The ready availability of software to quickly analyse these designs has made it possible to scrutinise claims made as to properties of eyepieces.  I believe it leads to a need for the reappraisal of many of the commonly held ideas about distortion characteristics of eyepiece ‘types’.

I will let people be their own judges.

I would like to repeat an earlier warning NOT to judge eyepieces simply on these distortion figures.  In some cases, the nicest looking distortion curves match with poor performance in other areas.

All of this begs the question of what is the best type of distortion characteristic for an eyepiece.  I think it depends a little on purpose and a lot on personal preferences and have no answer.

Others might like to comment here because one person’s preferences is just as valid as another.

Finally, I would like to apologise in advance for any errors.  If you find any, please let me know.