Apochromatic lens designs for astrotelescopes
In this section are described several designs for high performance lenses for telescopes being used with eyepieces.  The general specification is that the image field is 20mm diameter and axial and lateral aberration and the polychromatic modulation transfer function at an image spatial frequency of 100cycles/mm should exceed about 30% for focal ratios less than F/8.  Because the lenses will be used with an eyepiece, the eye focus setting can be used to compensate for some field curvature, but astigmatism is also to be within the tolerance.

The maximum aperture of the lenses is restricted to about 100mm.  Much above this, and the cost of the raw glass blanks begins to escalate without a significant increase in light-gathering or image sharpness.

The following lenses  are described:

(1)  A 600mm F/8 apochromat formed by a two element objective and a meniscus field flattener.
(2)  A 600mm F/6 apochromat formed by a three element objective and a meniscus field-flattener.
(3)  A 400mm F/4 apochromat formed by a three element objective and a meniscus field-flattener.

A common thread to these designs is the use of the SUMITA PFK85 'fluorite' glass and the SCHOTT  N-LAK10 glass.  This glass pair is remarkably well matched  for partial dispersion throughout the complete spectrum 0.45µm to 1.2µm.  Note however that if the full spectral range is required, then  it must be  SCHOTT N-LAK10.  There are between the identically named SUMITA and SCHOTT N-LAK10 glasses small but significant  differences in the fourth decimal place of the index value.
 
1.  The 600mm F/8 objective lens

The following image shows the air-spaced Fraunhofer ( 'flint' leading) configuration.  The relatively durable glass N-LAK10 is external and  protecting the rather more fragile PFK85.

                              
                                     

 The following image shows the meniscus field-flattening lens close to the focal position.

                                       

                                           
    
The following image shows that the lens is effectively diffraction limited over the full field of 1.9degrees.


            



This following image shows the remarkable 'apochromatic' correction of axial colour over the waveband accessible to the eye and to silicon based photodetectors.  Although the deviation seems high at about 250µm it must be remembered that the tolerance for defocus is in the region 600 wavelengths, i.e about 300µm.
              


The following table shows the prescription.  Notice that there is a common curvature on the objective elements- this saves tooling costs.
                                 




2.  The 600mm F/6 objective lens
A substantial increase in image brightness and resolveable frequencies, or a shortening of exposure time can be achieved by splitting the fluorite into two elements.  The excellent apochromatic correction is retained.
                     
                                                      

Notice the useful increase in MTF at 200cycles/mm as a result of the increase in numerical aperture.
This is the prescription. Notice that there are still only five curvature values, plus plano.



                                   

3.  The 400mm F/4  objective lens

The three element objective group design can be extended to a 400mm F/4 configuration, covering a field diameter of 2.9degrees.

         
                     

Although the performance is now no longer 'diffraction limited'  the PCMTF at 100cycles/mm is still in excess of 30%.  The apochromatism is also retained, but six curvature values are required,  plus plano.


                       


 



© Don Barron 2005