Satellite observation systems and reference systems (ae4-e01)

Signal Propagation

E. Schrama

Typical set-up satellite observation

• We measure range or range rates:– Ground station to ground station– Ground station to satellite or visa versa– Satellite to sea or land surface– In between satellites– Better than 1 cm accuracy often required

• Electromagnetic signals travel through a refractive medium (often no vacuum)

• As a result signal is delayed and this has certain consequences for satellite observation systems

Section 2.3 Seeber• Wave theory

– Frequency and wavelength– Amplitude and phase– Electromagnetic waves

• Antenna properties– Radio antennas, Microwave Antennas Optics, – Interference, Divergence angle antenna

• Modulation, phase and group speed• Refraction and Signal delay

– Dry tropospheric signal delay– Wet tropospheric signal delay– Ionospheric signal delay

• Examples– Observations with more frequencies– Models– Radiometers

Frequency and wavelength

fc

C: speed of light (approximately 3e8 m/s)

lambda: wavelength (meter, nanometer, Angstrom)

f: frequency (units: Hz, KHz MHz, GHz)

Bron: http://www.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html

Frequency and wavelength

Amplitude and phase).cos()( GtwHtx

Electro-Magnetic waves

Radio Antennas

Microwave antennas

Optics

Interference

Divergence angle antenna

Aperture

Lambda

Divergence angle = Lambda/Aperture

Refraction of signals• EM waves travel in vacuum at the speed of

light which we will call c• As soon as there is no more vacuum but

instead something else such as water or air then the propagation speed changes

• There is a difference between a group velocity and a phase velocity

• To understand this difference you must know something about the concept modulation

What is signal delay

l

s

dsnd

sntnctcd

ttn

tntv

ctt

ttvtcsv

cn

0

)1(

).1().1.(.

).1(

..)(

).(.

n: refractive index

t: geometric range delay

t: range delay term

v: group velocity of the signal

c: speed of light

l: geometric distance

s: observed distance

d: signal delay effect

transmitter

receiver

Modulation• To understand modulation

consider first a carrier which is nothing more than a signal with a constant frequency and amplitude

• To transfer information (data, music, spoken word, TV signals etc etc) you must do something with the carrier (like vary the amplitude of frequency or maybe both)

• The information signal is now modulated on the carrier

f

f f+gf-g

exp( jft ) * exp( jgt )

Modulation techniques

AM FM

Phase and Group speed

• Phase speed is for the carrier signal

• Group speed is for the modulated signal

• Information content is always transported with the group speed

• The phase speed may be faster than light (this is not a contradiction with the theory of relativity)

Relation group and phase velocity

• Rayleigh 1881 found the following relation:

• Velocity dispersion

• There is a similar relation for the refraction index

d

dvvv ppg

df

dnfnn pg

Refraction

2211 sinsin nn

Snellius law

Our distorted Sun including a blue flash

Ionospheric delay• The concentration of free electrons determines the

refractive index n• Ionospheric range delay is dispersive and thus depends on

the frequency of the signal. The delay is inversely proportional to the square of the frequency (ie. high frequencies have less ionospheric delay)

• Remedy: measure ranges at more than one frequency, • Linear combinations of ranges result in an ionospheric free

observation of the distance.

• Group and phase speeds have an opposite sign as far as the

ionospheric signal delay is concerned

What is the ionosphere?

• Ionisation of atmospheric gasses starts at circa 70 km height. Ions and free electrons are formed.

• Level of ionisation is determined by solar radiation and charged particles entering the Earth’s magnetic field. (Day/Night effect, and Solar wind are the main drivers)

• There are several layers in the ionosphere, short wave radio signals up to 30 MHz can reflect against these layers (AM and SW fading effects)

• Beyond 30 MHz signals always pass the ionosphere.

Image: Copyright the Regents of the University of Michigan

Example: ionospheric free combination

Ionospheric signal delay is inversely proportional to the frequency squared.

....

....

22

2

21

1

frd

frd

o

o

Ionospheric delay (JPL)

Tropospheric signal delay

• Troposphere: “everything below 100 km”• Dry tropospheric correction

– n is a function of properties of atmospheric gas d can be determined if air pressure is known

• Wet tropospheric correction– n is a function of water vapor content d to be determined by relative humidity (in-

situ, meteo model data or radiometer)

molK / / J 8.314:R

mol / kg 0.029: M

km) few a( :height scale

:upwards integrate

: substitute

:chydrostati pressure

:law gas ideal

)/(0

0

Mg

RT

ePP

RT

Mgdz

P

dP

gdzdPRT

MP

RTzMg

Barometric formula

This relation works perfectly for the dry

effect, for the wet effect it is a crude approximation

Radiometers and wet delay• A radiometer is nothing more than a radio receiver that

observes the amount of EM radiation of a particular object,

• Any object hotter than 0 K emits EM radiation, a radiometer therefor observes brightness temperatures (BT)

• At some frequencies (like 22 GHz) the opaqueness of the atmosphere is determined by water vapor

• By measuring the BT’s at frequencies around 22 GHz you can map the integrated water vapor content in a path.

• This technique is successfully applied on spaceborn radar systems and VLBI.

Gap water vapor absorption spectrum

Source: www.lsbu.ac.uk/water/vibrat.html

http://www.ca.astro.it/WEB-1/Proc_ESF/feist.pdf

Radiometer on T/P

Radiometric water vapor (JPL)