lenspl

R2026b

Refraction loss due to tropospheric lensing

Syntax

Llens = lenspl(sr,ht,el)

Llens = lenspl(___,Name=Value)

Description

Llens = lenspl(sr,ht,el) returns the Refraction Loss Due to Lensing along the propagated path as a function of straight-line slant range distance sr, height ht, and elevation angle el using the International Telecommunication Union (ITU) standard layered atmospheric model. The strong variation in refractivity versus altitude in the troposphere causes the atmosphere to act like a lens with loss independent of frequency.

Llens = lenspl(___,Name=Value) specifies additional inputs using name-value arguments. For example, you can specify the reference latitude model and water vapor density.

Examples

Plot Two-Way Lens Loss Curve

Calculate the two-way lens loss curve for a radar platform at sea level at an elevation angle of 0.03 deg over a slant range of 0.1 to 5.0 km.

h = 0; % m
el = 0.03; % deg 
R = (100:5000).*1e3; % m
L = 2*lenspl(R,h,el); % Factor of 2 for two-way propagation 

Plot the lens loss against the slant range.

plot(R.*1e-3,L);
xlabel('Range (km)');
ylabel('Loss (dB)');
title('Two-Way Lens Loss');

Input Arguments

sr — Slant range (m)

positive scalar | M-length positive vector

Slant range, or straight-line geometric distance between sensor and target, specified as a positive scalar or M-length positive vector. Units are in meters (m).

Data Types: single | double

ht — Height of radar relative to mean sea level (m)

nonnegative scalar in the range of [0,100000)

Height or altitude of radar relative to mean sea level (MSL), specified as a nonnegative scalar from 0 to 100000 m. Units are in meters (m).

Example: 2000

Data Types: single | double

el — Elevation angle of sensor (deg)

scalar | M-length real vector

Elevation angle of the sensor, specified as a scalar or M-length vector when sr is also an M-length vector. The elevation angle is the initial elevation angle of the ray leaving the sensor. A positive elevation angle points upwards toward the horizon (see Radar Coordinate Systems and Frames). The refraction loss due to lensing is set to zero for negative elevation angles. Units are in degrees (deg).

Example: 10

Data Types: single | double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

WaterVaporDensity — Standard ground-level water vapor density

7.5 (default) | positive scalar

Standard ground-level water vapor density, specified as a positive scalar. Applicable only for the default standard model (MAGRA). Units are in grams per meter cubed.

Data Types: single | double

ScaleHeight — Altitude above mean sea level

2e3 (default) | positive scalar

Altitude above mean sea level (MSL), specified as a positive waterscalar. Applicable only for the default standard model (MAGRA). For dry atmosphere conditions, set to 6e3 m. Units are in meters.

Data Types: single | double

LatitudeModel — Reference latitude model

'Standard' (default) | 'Low' | 'Mid' | 'High'

Reference latitude model, specified as one of these.

Model	Description
'Standard'(default)	This model is the mean annual global reference atmosphere (MAGRA) that reflects the mean annual temperature and pressure averaged across the world.
'Low'	This model is for low latitudes less than 22 degrees, where there is little seasonal variation.
'Mid'	This model is for mid latitudes between 22 and 45 degrees with seasonal profiles for 'Summer' and 'Winter', which can be specified using the 'Season' name-value argument.
'High'	This model is for high latitudes greater than 45 degrees with seasonal profiles for 'Summer' and 'Winter', which can be specified using the 'Season' name-value argument.

Season — Season

'Summer' (default) | 'Winter'

Season for the 'Mid' and 'High' latitude models, specified as 'Summer' or 'Winter'. Other models ignore this input. Defaults to 'Summer'.

AtmosphereMeasurements — Custom atmospheric measurements

N-by-4 matrix

Custom atmospheric measurements for the calculation of the refractive index, specified as an N-by-4 matrix, where N corresponds to the number of altitude measurements. N must be greater than or equal to 2. The first column is the atmospheric temperature in kelvins, the second column is the atmospheric pressure in hPa, the third column is the water vapor density in g/m³, and the fourth column is the MSL altitude of the measurements in meters. When you use a custom model, all other name-value arguments are ignored and the output refractive index is applicable for the input height.

Note

The Layered Atmosphere Model assumes geometrical optics conditions, as a result anomalous propagation like ducting and subrefraction cannot be present in provided measurements. If atmospheric measurements evidencing ducting and subrefraction are provided, this function throws an error.

Data Types: single | double

Output Arguments

Llens — One-way refraction loss due to lensing (dB)

M-length vector

One-way refraction loss due to tropospheric lensing, returned as an M-length vector. A value of 0 is returned when el is negative. The lensing loss can be significant for small elevation angles and long ranges. Lensing loss is not due to a dissipation of energy and therefore does not contribute to the system noise temperature. Units are in decibels (dB).

Data Types: double

More About

Refraction Loss Due to Lensing

Radar frequency signals refract due to vertical gradients in the atmospheric refractive index, which bends the propagation path downward. In addition, the variation in refraction versus altitude makes the atmosphere act like a lens that defocuses or spreads the beam, with loss independent of frequency. Rays leaving an antenna at positive elevation angles are refracted in the troposphere and the energy radiated within some angular extent is distributed over a slightly greater angular sector, thereby reducing the energy density relative to free-space propagation [1] [3].

lenspl calculates the lensing loss as the derivative of the final elevation angle of the signal with respect to the initial elevation angle EL, where the final elevation angle is calculated from the Layered Atmosphere Model.

Lensing loss is a function of range and elevation angle and can be significant at long ranges and shallow elevation angles, especially for a low-altitude sensor.

References

[1] Weil, T. A. "Atmospheric Lens Effect: Another Loss for the Radar Range Equation". IEEE Transactions on Aerospace and Electronic Systems Vol. AES-9, No. 1 (Jan. 1973).

[2] International Telecommunication Union (ITU). "Attenuation by Atmospheric Gases and Related Effects". Recommendation ITU-R P.676-12, P Series, Radiowave Propagation (Aug 2019).

[3] Meikle, H. Modern Radar Systems. 2nd edition. Norwood, MA: Artech House, 2008.

[4] Barton, David K. Radar Equations for Modern Radar. 1st edition. Norwood, MA: Artech House, 2013.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021a