A telescope is an information acquisition system, not a magnification system.

##  Star sizes in Angular Diameter (arcsecond)

Use Jupiter as example, angular diameter is:$$θ≈\frac{\text{physical size}}{\text{distance}}≈\frac{d}{R}$$Jupiter diameter d=142,984 km, R≈628,000,000 km.
$$θ=\frac{142,984​}{628,000,000} =2.28×10^{−4} rad= 47^"$$
Information / signal of Jupiter → photons → Earth → telescope.

---
### 1. Aperture - information / signal capture
	This is the most important parameter

For 127 SLT, aperture D = 127 mm, the collection area is:
$$A=π(63.5)^2 A≈12668 mm^2≈126.7 cm^2$$
As compared to human eye's pupil, D=7 mm.
$$
A_{eye}=38.5 mm^2
$$
Thus:
$$
\frac{12668}{38.5} \approx329

$$
The 127SLT gets 329X more light than human eye.

**Angular information**
When a photon (particle + wave) passes through a finite aperture (127 mm opening), diffraction occurs (imagine water passing through a gap). 

Rayleigh criterion:
![[Pasted image 20260620130814.png|389]]
$$θ=1.22 \frac{λ}{D}​$$
where D=127 mm, λ = 550 nm (as an example). 1 arcsecond = 4.84814e-6 rad.
$$θ≈1.06^{′′}$$
Dawes observed in practice, telescope normally resolve better, thus:
$$θ=\frac{116}{D}=\frac{116}{127}​=0.91^{′′}$$
Conclusion: a perfect point source is smeared over around 1 arcsecond.

---
### 2. Image at focal plane - Information encoding
Different incoming angles map to different focal-plane positions.
$$x=fθ$$
where:
- x = position on focal plane
- f = focal length
- θ = incoming sky angle


The 127SLT has f=1500 mm, and 1 arcsec=4.848×10−6 rad, therefore: 
$$x=1500×4.848×10^{−6} =0.00727 mm = 7.27 μm$$
Hence on 127SLT:
$$ 1 arcsec = 7.27 μm$$
Taking Jupiter as example, use angular diameter = 40′′.
$$h=1500×40×4.848×10^{−6} h=0.291 mm = 291 μm$$
So Jupiter image inside the telescope is 291 μm at the focal plane.

---
### 3. Image observation - CMOS/ eyepiece.
#### 3.1 CMOS mode
No eyepiece, no magnification, focal plane directly sits on CMOS.
Use Jupiter as example, the image size = 291 μm. Nikon Z5 II has pixel size of 5.9 μm, therefore **Jupiter appears as roughly 49 pixels**. 
$$\text{Image Scale}=206265×\frac{\text{Pixel Size(μm)}}{\text{Focal Length(mm)}}$$​Where 1 rad = 206265 arcseconds, therefore for Z5 II:
$$206.265×\frac{5.9} {1500}=0.81^{′′}/\text{pixel}$$
Recall that 127SLT diffraction limit ≈0.91′′ and camera sample 0.81′′/pixel, **so the camera is capturing nearly all the spatial information available from the telescope**.
#### 3.2 Eyepiece mode
Use 25 mm eyepiece as example, this gives magnification of:
$$M=\frac{1500}{25}​=60×$$
Similarly 10 mm eyepiece is going to give 150× magnification, but more magnification is just displaying larger image with the same detail.

This means if Jupiter contains a tiny storm of 0.3", and since 127SLT has resolution of 0.91", this storm will never be resolved on the focal plane hence eyepiece cannot display it regardless of magnification.

The telescope exit pupil for 25 mm eyepiece is:$$\text{Exit Pupil}=\frac{\text{Aperture}}{\text{Magnification}}=\frac{127mm}{60}=2.1mm$$The eyepiece produces a 2.1 mm beam.​ Similarly for a 5 mm eyepiece, only a 0.42 mm light beam will be produced. 

But human eye pupil has d = 7mm, for 0.42 mm beam, only a small fraction of pupil is used.
#### 3.3 Barlow Lens
Effectively a pre-eyepiece, a 2X Barlow lens make 127SLT effectively a 3000mm focal length but does not change the intrinsic resolution of the telescope.
Similarly, other magnifying units such as telecentric amplifier are structurally complicated with effective outcome as a Barlow.
### 4. Complete information flow
```
Jupiter
    │
    ▼
 Photons
(Intensity + Angle)

    │
    ▼
=================
127 mm Aperture
=================
Determines:
- Photon count
- SNR
- Resolution
- Information capacity
    │
    ▼
=================
1500 mm Optics
=================
Converts:
Angle → Position
x = fθ
    │
    ▼

Real Image
(Jupiter ≈ 0.29 mm)

    │
 ┌──┴──┐
 ▼     ▼
CMOS  Eyepiece

Record Display
    │
    ▼
Human Brain
```