Comparative Messier Digital Object Sketches With 11x80 Chinon, 20x100 Apogee and a Tasco 60mm/700mm

Version 1.2.1b2 of 13/2/2021-11:25 p.m.

On this page the author is attempting a careful electronic sketch simulation of what he saw while on the Antiparos island, with his Equipment.

The author is more concerned with giving the sketches a realistic appearance, i.e. for them to represent well what an observer sees through the above equipment[1].

All the sketches were digitally processed using Photoshop from observations made on average 6.7+ skies. Contrast and brightness have been changed sometimes globally, sometimes locally and extended star images have been anti-aliased, where applicable. The author is paying more attention to extended objects and not star images[2], aiming at a realistic simulation.

Calculations for the digital processing assume correct fields of vision of all three instruments and changes in brightness according to what the author saw, in most cases. Occasionally, field edges have been cropped, to save space and time. The processing has been done on a Presario 2100 laptop with its screen at full brightness.

All pictures below:

  1. Left: 11x80 Chinon binoculars.
  2. Middle: 20x100 giant Apogee binoculars.
  3. Right: Tasco 60mm/700mm @56x.


M31-M32-M110 (Andromeda Galaxy and satellites) in Andromeda

M31 with 11x80 M31 with 20x100 M31 with Tasco @35x

M51 (Whirlpool Galaxy) in Canes Venatici

M51 with 11x80 M51 with 20x100 M51 with Tasco @35x

M8 (Lagoon Nebula) in Sagittarius

M8 with 11x80 M8 with 20x100 M8 with Tasco @35x

M22 in Sagittarius

M22 with 11x80 M22 with 20x100 M22 with Tasco @35x

M57 (Ring Nebula) in Lyra (Tasco@80x)

M57 with 11x80 M57 with 20x100 M57 with Tasco @80x

M33 (Triangulum Galaxy) in Triangulum

M33 with 11x80 M33 with 20x100 M33 with Tasco @35x

M81-M82 in Ursa Major

M81/82 with 11x80 M81/82 with 20x100 M81/82 with Tasco @35x

M92 in Hercules

M92 with 11x80 M92 with 20x100 M92 with Tasco @35x

M27 (Dumbbell Nebula) in Vulpecula

M27 with 11x80 M27 with 20x100 M27 with Tasco @35x

M1 (Crab Nebula) in Taurus

M1 with 11x80 M1 with 20x100 M1 with Tasco @35x

NGC 7293 (Helix Nebula) in Aquarius

NGC7293 with 11x80 NGC7293 with 20x100 NGC7293 with Tasco @35x

M11 (Wild Ducks Cluster) in Scutum

M11 with 11x80 M11 with 20x100 M11 with Tasco @35x

Some Useful Theoretics[3]

Magnification: Mx=Dfl/EPfl
Exit pupil: Dep=Ds/Mx[5]
Actual exit pupil: Dep*=min{EYEexitp, Dep}
Transmission factor: θ~ 64% for refractors, 67% for reflectors[4]
Raw light grasp brightness: G=θ*Ds2/Dep2
Relative brightness: RB = θ*Ds2/(Dep*)2*Mx2
Telescopic brightness: Btel= θ*Ds2/(Dep*)2/Mx2
Magnitudes per aperture inch (γ): γ*Ds=Mx
Relative telescopic brightness: RBtel=θ/(γ*Dep*)2

Using the above, we can generate a table which compares between different Ds' and Mx's with Maple code:

Dobj := [25.4, 76.2, 88.9, 101.6, 120.7, 152.4, 203.2, 254.0, 304.8];#list of Ds'
M := [6, 8, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150];#list of Mx's
ps := "%";
for r to nops(M) do
for c to nops(Dobj) do
printf("%6.2f%1s", 100*RBtel(1, 7, Dobj[c], M[r])*Dexitp(Dobj[c], M[r])
/(RBtel(1, 7, Dobj[nops(Dobj)], M[1])*Dexitp(Dobj[nops(Dobj)], M[r])), ps)
end do;
printf("\n")
end do;

Relative Telescopic Brightness (constant θ for all)

Dobj (in)[6] 1 3 3.5 4 4.75 6 8 10 12
Dobj (mm) 25.4 76.2 88.9 101.6 120.7 152.4 203.2 254.0 304.8
6x 0.06% 1.56% 2.48% 3.70% 6.20% 12.50% 29.63% 57.87% 100%
8x 0.03% 0.88% 1.40% 2.08% 3.49% 7.03% 16.67% 32.55% 56.25%
10x 0.02% 0.56% 0.89% 1.33% 2.23% 4.50% 10.67% 20.83% 36.00%
20x 0.01% 0.14% 0.22% 0.33% 0.56% 1.13% 2.67% 5.21% 9.00%
30x 0.00% 0.06% 0.10% 0.15% 0.25% 0.50% 1.19% 2.31% 4.00%
40x 0.00% 0.04% 0.06% 0.08% 0.14% 0.28% 0.67% 1.30% 2.25%
50x 0.00% 0.02% 0.04% 0.05% 0.09% 0.18% 0.43% 0.83% 1.44%
60x 0.00% 0.02% 0.02% 0.04% 0.06% 0.13% 0.3% 0.58% 1.00%
70x 0.00% 0.01% 0.02% 0.03% 0.05% 0.09% 0.22% 0.43% 0.73%
80x 0.00% 0.01% 0.01% 0.02% 0.03% 0.07% 0.17% 0.33% 0.56%
90x 0.00% 0.01% 0.01% 0.02% 0.03% 0.06% 0.13% 0.26% 0.44%
100x 0.00% 0.01% 0.01% 0.01% 0.02% 0.05% 0.11% 0.21% 0.36%
110x 0.00% 0.00% 0.01% 0.02% 0.02% 0.04% 0.09% 0.17% 0.30%
120x 0.00% 0.00% 0.01% 0.01% 0.02% 0.03% 0.07% 0.14% 0.25%
130x 0.00% 0.00% 0.01% 0.01% 0.01% 0.03% 0.06% 0.12% 0.21%
140x 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.05% 0.11% 0.18%
150x 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.05% 0.09% 0.16%

Perceived Relative Telescopic Brightness (constant θ for all)

The eye's light response stimulus curve is logarithmic[3]. Adjusting the above to an arbitrary brightness scale from 0 to 10 (brightest: - 12"@6x), we get[6]:

Dobj (in)[6] 1 3 3.5 4 4.75 6 8 10 12
Dobj (mm) 25.4 76.2 88.9 101.6 120.7 152.4 203.2 254.0 304.8
6x 6.76 8.19 8.39 8.57 8.79 9.10 9.47 9.76 10.00
8x 6.51 7.94 8.14 8.32 8.54 8.85 9.22 9.51 9.75
10x 6.32 7.75 7.95 8.12 8.35 8.65 9.03 9.32 9.56
20x 5.72 7.15 7.35 7.52 7.75 8.05 8.43 8.72 8.95
30x 5.36* 6.80 7.00 7.17 7.40 7.70 8.07 8.36 8.60
40x 5.11 6.55 6.75 6.92 7.15 7.45 7.82 8.11 8.35
50x 4.92 6.35 6.55 6.73 6.95 7.26 7.63 7.92 8.16
60x 4.76 6.19 6.39 6.57 6.79 7.10 7.47 7.76 8.00
70x 4.63 6.06 6.26 6.43 6.66 6.96 7.34 7.63 7.87
80x 4.51 5.94 6.14 6.32 6.54 6.85 7.22 7.51 7.75
90x 4.41 5.84* 6.04 6.22 6.44 6.74 7.12 7.41 7.65
100x 4.32 5.75 5.95 6.12 6.35 6.65 7.03 7.32 7.56
110x 4.24 5.67 5.87* 6.04 6.27 6.57 6.95 7.24 7.47
120x 4.16 5.59 5.79 5.97 6.19 6.49 6.87 7.16 7.40
130x 4.09 5.52 5.72 5.90* 6.12 6.43 6.80 7.09 7.33
140x 4.03 5.46 5.66 5.83 6.06 6.36 6.74 7.03 7.26
150x 3.97 5.40 5.60 5.77 6.00* 6.30 6.68 6.97 7.20

Arbitrary Comparisons

Locate your scope on the table above, using your Dobj and required nagnification Mx and compare between the values on the corresponding entries. For example, for the three instruments on this page: Tasco at Mx=60mm@56x=700/12.5~6.1, Chinon 11x80~7.7 (Because of measured Vignette its objective is closer to 76mm really) and Apogee 20x100~7.5 (without having yet measured Vignette). In practical terms the previous mean that on the same DSO extended target at the aforementioned magnifications, the Chinon's image would be about 7.7-6.1=1.6 unit times brighter than that of the Tasco and about 7.7-7.5=0.2 unit times brighter than that of the Apogee, with the latter being 7.5-6.1=1.4 unit times brighter than the Tasco's, on an arbitrary brightness unit scale from 1 to 10, with 10 being the reference perceived full brightness of a 12"@6x of the same DSO[7].

Notes/References

  1. For the full observing reports, consult the two articles on 11x80 and 20x100.
  2. Only some of the brightest stars are shown in the sketches. It is practically impossible to include all stars seen on a given field of view with the 11x80 and 20x100 pairs, because the latter easily show stars down to magnitude 11.5, sometimes even lower, so the number of visible stars is confounding.
  3. References: usenet: [1], [2], [3], [4]. Also, this and this web posts and this book.
  4. Ref. [1] above, has more optimistic values for θ. See last book ref. above.
  5. Also depending on Vignette on refractors and other factors, such as area of front surface obstruction on reflectors and catadioptrics, etc.
  6. (*) indicative of maximum practical magnification that can be achieved for this Dobj size for a minimum non-zero contrasted image for extended DS objects. For stars and planets, still valid, but with reduced values. Comparing brightness values below this one on any column entry for most non point sources would be meaningless.
  7. For comparing between different types of instruments, you can use the expression from the Maple code with θ12 < 1 on the numerator and denominator and then log-normalize the results.

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