K3's Astronomy - Telescopes
"When I consider your heavens, the work of your fingers, the moon and the stars which You have set in place, what is Man that You are mindful of him?" -- Psalm 8:3,4
1. Barlow Lens

Barlow lens is used for extending focal length of telescope objective. It is diverging lens.

F - original objective focus position
F' - new position of focus
fB - focal length of Barlow lens
fO - focal length of objective

FE - extending facor of Barlow Lens (FE>1)
For such optical system there is an equation:

-1/d1 + 1/d2 = -1/fB            (1.1)

d1 . d2 = fB.d2 - fB.d1          (1.2)

For extendending factor of Barlow lentgh there is:

FE = d2 / d1                        (1.3)

So from (1.2) and (1.3) there is:

FE = 1 + d2 / fB                  (1.4)

FE = fB / (fB - d1)                (1.5)

The result focal length of telescope with objective with fO is:

f = fO . FE = fO . (1 + d2 / fB)           (1.6)

If magnification factor of Barlow lens is N (thus FE = N), then

d2 = (N-1) . fB                   (1.7)

d1 = (1-1/N) . fB                (1.8)

For given lens with fB (and d2 calculated according to 1.7) the next equation can be useful:

d1 = fB.d2 / (fB + d2)           (1.9)

Distance between CCD position in prime focus and CCD position in focus with Barlow lens is Dd:

Dd = d2 - d1 = d2 - d2 / N = d2 . (1 - 1/N)

As d2 ~ lB (lB is distance between Barlow diverging lens and top of Barlow), then

Dd ~ lB . (1 - 1/N)                (1.10)

2. Focal reducer

Focal reducer is used for reducing focal length of telescope objective. It is converging lens. It helps to increase "speed" of the telescope.

F - original objective focus position
F' - new position of focus
fR - focal length of focal reducer lens
fO - focal length of objective

FE - extending facor of focal reducer (FE<1)
For such optical system there is an equation:

-1/d1 + 1/d2 = 1/fR              (2.1)

d1 . d2 = fR.d1 - fR.d2          (2.2)

For extendending factor of focal reducer lentgh there is:

FE = d2 / d1                        (2.3)

So from (2.2) and (2.3) there is:

FE = 1 - d2 / fR                   (2.4)

FE = fR / (fR + d1)              (2.5)

The result focal length of telescope with objective with fO is:

f = fO . FE = fO . (1 - d2 / fR)           (2.6)

If reducing factor of focal reducer is N (thus FE = N), then

d2 = (1 - N) . fR                 (2.7)

d1 = (1/N - 1) . fR              (2.8)

For given lens with fR (and d2 calculated according to 2.7) the next equation can be useful:

d1 = fR.d2 / (fR - d2)           (2.9)

Distance between CCD position in prime focus and CCD position in focus with focal reducer is Dd:

Dd = d1 - d2 = d2 / N - d2 = d2 . (1/N - 1)

As d2 = lR (lR is distance between focal reducer lens and CCD), then

Dd = lR . (1/N - 1)                (2.10)

Using (2.9) we get:

Dd = lR2 / (fR - lR)                 (2.11)
With focal reducer it is possible to shorten exposure time by 1/FE2 times (FE<1). If the limited factor of exposure length is mount drift, the exposure time can be extended by 1/FE times. That means that total exposure of the picture will increase by 1/FE3 times, while picture quality remains the same (if we consider star drift). The image size will decrease by 1/FE times and field of view will increase by 1/FE times.

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Last Update: 11.11.2001