Synthetic Aperture Radar (SAR) Imaging

A synthetic aperture radar (SAR) is an imaging radar carried on an aircraft or satellite. It transmits microwave pulses sideways as it moves, records the amplitude and phase of the echoes, and combines the echoes received along its path into an image. The combination acts like an antenna much longer than the physical one, which is the “synthetic aperture” of the name (Moreira et al., 2013). Because it brings its own illumination, at wavelengths of centimetres to a metre, SAR images by day and night and through cloud.

For computer vision, a SAR image differs from a photograph in almost every respect. Its pixels are complex numbers, not intensities. Its two axes are along-track position and distance from the sensor, not angles through a lens. Its brightness depends on surface roughness, geometry and moisture rather than on colour. And it is covered in speckle, a granular pattern that comes from the physics of coherent imaging rather than from the detector. Remote sensing introduces SAR in outline among the other Earth observation sensors. This article covers image formation, the data products, speckle, geometric distortions, polarimetry and interferometry, and the public missions.

How It Works

Side-looking geometry and the radar equation

The radar looks to one side of its track. The flight direction is called azimuth (or along-track) and the line of sight slant range; the projection of slant range onto the ground is ground range (Moreira et al., 2013). The radar emits pulses at a pulse repetition frequency (PRF) of a few hundred to a few thousand hertz and, between pulses, listens for echoes. Time within one echo is called fast time and corresponds to range; the time between pulses is called slow time and corresponds to azimuth. The recorded data form a two-dimensional matrix of complex samples, one row per pulse.

How much power returns is described by the radar equation. In Doerry’s (2006) form, the received power for a single pulse is

$$P_r = \frac{P_t\, G_A\, A_e\, \sigma}{(4\pi)^2 R^4 L_\text{radar} L_\text{atmos}},$$

where $P_t$ is the transmitted power, $G_A$ the antenna gain, $A_e$ the effective receiving area of the antenna, $\sigma$ the target’s radar cross section (m²), $R$ the range, and the $L$ terms are losses in the radar and the atmosphere. Dividing by the thermal noise power $kTF_NB_N$ (Boltzmann’s constant, noise temperature, receiver noise factor and noise bandwidth) gives the signal-to-noise ratio at the antenna. Processing then multiplies it by two gains, $G_r$ from pulse compression in range and $G_a$ from coherently combining many pulses in azimuth, giving the image signal-to-noise ratio $\text{SNR}_\text{image} = \text{SNR}_\text{antenna}\, G_r G_a$, the relation Doerry calls the radar equation. For distributed targets such as fields or forest, the cross section is the reflectivity per unit area, $\sigma^0$, times the ground area of the resolution cell (Doerry, 2006). By our reading, the $R^4$ explains why a spaceborne radar needs large antennas, high power and long integration, and the processing gains show that focusing matters for noise as well as for resolution.

Range resolution and pulse compression

Two echoes can be separated in range if they do not overlap in time. A short pulse of length $\tau_p$ gives a slant-range resolution of $c\tau_p/2$, the factor 2 coming from the round trip (Meyer, 2019). Short pulses carry little energy, so SAR systems instead transmit long, linearly frequency-modulated pulses, called chirps, whose instantaneous frequency sweeps a bandwidth $B_r$ over the pulse (Moreira et al., 2013). After matched filtering, the slant-range resolution depends only on the bandwidth:

$$\delta_r = \frac{c}{2B_r}.$$

Matched filtering correlates each received line with the transmitted chirp. Moreira et al. note that it is done as a multiplication in the frequency domain, by the complex conjugate of the chirp’s spectrum, because that is far cheaper than convolution in the time domain; this is the convolution theorem of the Fourier transform at work. On the ground, the resolution is coarser than in slant range by the factor $1/\sin\theta_i$, where $\theta_i$ is the local incidence angle, so ground-range resolution improves away from nadir, the opposite of an optical scanner (Meyer, 2019).

Azimuth resolution and aperture synthesis

A real antenna of length $d_a$ has a beamwidth of about $\lambda/d_a$. A side-looking airborne radar (SLAR) without aperture synthesis can separate two targets in azimuth only if they are not in the beam at the same time, so its azimuth resolution is the footprint $\lambda r_0/d_a$, which grows with range $r_0$. Moreira et al. give the example of an X-band SLAR with a 3 m antenna at 5 km range: a beamwidth of 0.01 rad and an azimuth resolution of 50 m. Meyer (2019) shows that the same principle applied from orbit would need an antenna hundreds of metres long.

Aperture synthesis removes the dependence on range. A point on the ground stays in the beam while the platform travels a distance $L_{sa} = \lambda r_0/d_a$, the synthetic aperture. Over that path, its range follows

$$r(t) = \sqrt{r_0^2 + (vt)^2} \approx r_0 + \frac{(vt)^2}{2r_0},$$

and the echo’s phase changes as $\varphi(t) = -4\pi r(t)/\lambda$ (Moreira et al., 2013). The phase history is quadratic, so the azimuth signal is itself a chirp, with instantaneous Doppler frequency $f_D(t) = -2v^2t/(\lambda r_0)$. Matched filtering this azimuth chirp yields a resolution

$$\delta_a = \frac{d_a}{2},$$

independent of range and of wavelength (Moreira et al., 2013). The counter-intuitive consequence is that a shorter antenna gives finer azimuth resolution: its wider beam keeps each target in view longer, which synthesizes a longer aperture. The price is sampling. The PRF must exceed the Doppler bandwidth $2v/d_a$, so the platform may move at most half an antenna length between pulses (Moreira et al., 2013). A higher PRF leaves less time to receive the echoes of one pulse before the next is sent, which narrows the swath. Fine azimuth resolution and a wide swath therefore conflict in a conventional single-channel SAR, and violating the limits produces ambiguities, features that appear at wrong or multiple positions in the image; it is the radar form of aliasing.

Imaging modes trade these quantities by steering the antenna beam (Moreira et al., 2013). Stripmap keeps the beam fixed and images one continuous strip. ScanSAR switches the beam between several sub-swaths for a wider swath at coarser azimuth resolution. Spotlight steers the beam to stay on one patch, lengthening the synthetic aperture for finer resolution but giving up continuous coverage. Terrain Observation with Progressive Scans (TOPS), the mode Sentinel-1 uses over land, steers the beam in azimuth during each burst to avoid the uneven brightness of ScanSAR (ESA, S1 Mission).

Focusing

Raw SAR data show no recognizable scene (Moreira et al., 2013): each target’s energy is spread over a pulse length in range and a synthetic aperture in azimuth. Focusing compresses it back. In the simplest description, it is two matched filters, one along range with the transmitted chirp as reference and one along azimuth with the expected response of a point target, which depends on range (Moreira et al., 2013). The complication is range cell migration: the range to a target changes by $(vt)^2/(2r_0)$ during the aperture, so its echoes curve through several range cells when that change exceeds about half a range resolution cell. Because the curvature depends on $r_0$, accurate focusing is a two-dimensional, space-variant filtering problem. Moreira et al. name the main families of algorithms developed for it: wavenumber-domain ($\omega$–$k$) processors, range–Doppler algorithms and chirp scaling.

The script below simulates the raw data of a single point target and focuses it with two FFT-based matched filters. The parameters are illustrative, chosen to keep the example small: the C-band wavelength of Sentinel-1 (5.55 cm), a 4 m antenna at 10 km range on a platform moving at 100 m/s, and a 50 MHz chirp. The antenna pattern is modelled as a hard cut-off over the synthetic aperture. Range migration over the aperture is about 0.24 m, below half the 3 m range resolution, so no migration correction is needed. The script measures the half-power width of the focused response, which Moreira et al. use as the definition of resolution, and the gain in signal-to-noise ratio from focusing, using complex white noise passed through the same processor. It runs with NumPy 2.3.5.

import numpy as np

c, lam, da = 3e8, 0.0555, 4.0           # speed of light, C-band wavelength, antenna length (m)
r0, v, prf = 10e3, 100.0, 62.5          # closest range (m), platform speed (m/s), PRF (Hz)
B, tau, fs = 50e6, 5e-6, 60e6           # chirp bandwidth, pulse length, complex sampling rate
Nr, Na = 1024, 512                      # range samples, pulses
K = B / tau                             # chirp rate (Hz/s)
L = lam * r0 / da                       # synthetic aperture length (m)

t = (np.arange(Nr) - Nr // 2) / fs + 2 * r0 / c       # fast time
x = (np.arange(Na) - Na // 2) * v / prf               # platform position along track
R = np.sqrt(r0**2 + x**2)                             # range history of a target at x = 0
d = t[None, :] - 2 * R[:, None] / c                   # delay relative to each echo
raw = ((np.abs(d) <= tau / 2) * (np.abs(x)[:, None] <= L / 2)
       * np.exp(1j * np.pi * K * d**2) * np.exp(-4j * np.pi * R[:, None] / lam))

def focus(data):
    tr = (np.arange(Nr) - Nr // 2) / fs
    chirp = (np.abs(tr) <= tau / 2) * np.exp(1j * np.pi * K * tr**2)
    rc = np.fft.ifft(np.fft.fft(data, axis=1) * np.conj(np.fft.fft(np.fft.ifftshift(chirp))), axis=1)
    ref = (np.abs(x) <= L / 2) * np.exp(-4j * np.pi * np.sqrt(r0**2 + x**2) / lam)
    return np.fft.ifft(np.fft.fft(rc, axis=0) * np.conj(np.fft.fft(np.fft.ifftshift(ref)))[:, None], axis=0)

def width_3db(cut, spacing, up=16):     # half-power width of a band-limited 1-D cut
    F = np.fft.fftshift(np.fft.fft(cut))
    pad = np.zeros(len(cut) * up, complex)
    pad[(len(pad) - len(cut)) // 2:(len(pad) + len(cut)) // 2] = F
    p = np.abs(np.fft.ifft(np.fft.ifftshift(pad))) ** 2
    return (p >= p.max() / 2).sum() * spacing / up

img = focus(raw)
ia, ir = np.unravel_index(np.abs(img).argmax(), img.shape)
n_r, n_a = int(round(tau * fs)), int((np.abs(x) <= L / 2).sum())
print("raw echo spread over %d range samples x %d pulses" % (n_r, n_a))
print("range:   -3 dB width %.2f m   c/2B = %.2f m   pixel %.2f m"
      % (width_3db(img[ia, :], c / (2 * fs)), c / (2 * B), c / (2 * fs)))
print("azimuth: -3 dB width %.2f m   da/2 = %.2f m   pixel %.2f m"
      % (width_3db(img[:, ir], v / prf), da / 2, v / prf))

rng = np.random.default_rng(0)
noise = (rng.standard_normal(raw.shape) + 1j * rng.standard_normal(raw.shape)) / np.sqrt(2)
gain = np.abs(img[ia, ir]) ** 2 / np.mean(np.abs(focus(noise)) ** 2)   # raw SNR is 1
print("SNR gain %.1f dB   samples combined %d (%.1f dB)"
      % (10 * np.log10(gain), n_r * n_a, 10 * np.log10(n_r * n_a)))

raw echo spread over 300 range samples x 87 pulses
range:   -3 dB width 2.81 m   c/2B = 3.00 m   pixel 2.50 m
azimuth: -3 dB width 1.70 m   da/2 = 2.00 m   pixel 1.60 m
SNR gain 44.1 dB   samples combined 26100 (44.2 dB)

The target’s energy, spread over 300 range samples and 87 pulses in the raw data, is gathered into a response about one pixel wide in each direction. The measured widths fall slightly below $c/2B_r$ and $d_a/2$. That is expected, by our reasoning: the formulas give the inverse of the bandwidth, while the half-power width of an unweighted, sinc-shaped response is about 0.89 of it; the chirp’s finite length and the 1/16-pixel measurement grid account for the remaining differences. Operational processors weight the spectrum to lower the sidelobes, which widens the response (Doerry, 2006, allows for it with a broadening factor of typically about 1.2): Sentinel-1’s IW high-resolution ground-range product lists Hamming weighting coefficients of 0.70 to 0.75 in range and azimuth (ESA, S1 Products). The gain in signal-to-noise ratio equals the number of samples combined coherently, 300 × 87, within the precision of the noise estimate. That is the product $G_rG_a$ of the radar equation.

Data It Produces

A focused image is a matrix of complex numbers in slant range and azimuth, a single-look complex (SLC) image. Its magnitude is the amplitude, its square the intensity, and its phase, useless on its own because it varies randomly from pixel to pixel, becomes informative when two images are compared (see Interferometry below). Sentinel-1’s SLC products keep one look in each dimension at full bandwidth, in slant-range geometry. Its ground-range detected (GRD) products are detected (only amplitude is kept), multilooked and projected to ground range on the WGS84 ellipsoid, with approximately square pixels and reduced speckle at the cost of resolution (ESA, S1 Processing).

The table gives Sentinel-1’s product characteristics for its main land mode and its stripmap mode, as ESA lists them (ESA, S1 Products, as of October 2026). GRD resolutions are mid-range values averaged over the swaths; SLC values run from the lowest to the highest incidence angle.

Mode	Product	Resolution, range × azimuth	Pixel spacing	Looks, range × azimuth	ENL
IW	SLC	2.7 × 22 to 3.5 × 22 m (slant range)	2.3 × 14.1 m	1 × 1	1
IW	GRD high resolution	20 × 22 m	10 × 10 m	5 × 1	4.4
IW	GRD medium resolution	88 × 87 m	40 × 40 m	22 × 5	81.8
SM	GRD full resolution	9 × 9 m	3.5 × 3.5 m	2 × 2	3.7
SM	GRD medium resolution	84 × 84 m	40 × 40 m	22 × 22	398.4

The last column, the equivalent number of looks, is explained under speckle below. For the multilooked products, its values are below the nominal number of looks.

Pixel values are calibrated to physical backscatter. Moreira et al. describe calibration as making the intensity represent $\sigma^0$, the radar cross section normalized to area, using internal instrument calibration and external targets of known reflectivity. Sentinel-1 Level-1 products carry calibration look-up tables that convert pixel values to $\beta^0$, $\sigma^0$ or $\gamma$, and thermal noise vectors that can be scaled by the same tables and subtracted from ground-range products (ESA, S1 Processing). Backscatter is usually displayed in decibels, $10\log_{10}\sigma^0$; the logarithm compresses a range of several orders of magnitude, and, by our reasoning, it also turns the multiplicative speckle described next into an additive term, which is why many vision pipelines work on log intensity.

Characteristics

Speckle

Each resolution cell of a natural surface contains many elementary scatterers, and the echo is their coherent sum. When no scatterer dominates, the real and imaginary parts of the sum are independent zero-mean Gaussian variables by the central limit theorem, a condition called fully developed speckle (Argenti et al., 2013). The amplitude then follows a Rayleigh distribution, the phase is uniform, and the intensity $I$ is exponential with mean equal to the cell’s reflectivity $\sigma$:

$$p(I \mid \sigma) = \frac{1}{\sigma} e^{-I/\sigma}, \qquad I = \sigma u, \quad p(u) = e^{-u}.$$

This is the multiplicative model of speckle: an exponential variable $u$ with unit mean multiplies the reflectivity (Argenti et al., 2013). The standard deviation of single-look intensity equals its mean, so bright areas fluctuate more than dark ones, and a uniform field looks grainy. Moreira et al. stress that speckle is not noise in the usual sense. It is a physical measurement of the structure of the resolution cell below the resolution, and it cannot be reduced by transmitting more power. Meyer (2019) notes that, unlike most noise sources, it depends on image brightness, which makes it hard to treat. Point targets, where one scatterer dominates, do not follow this model; their amplitude follows a Rice distribution and speckle filters treat them separately (Argenti et al., 2013). Ultrasound imaging shares the coherent mechanism, though Argenti et al. point out that weak ultrasound echoes add electronic noise that the SAR model can neglect.

Multilooking and the equivalent number of looks

Averaging $L$ independent intensity values of the same area keeps the mean $\sigma$ and divides the variance to $\sigma^2/L$; the result follows a gamma distribution (Argenti et al., 2013). The looks can come from splitting the Doppler bandwidth during processing into sub-apertures, each focused separately, or from averaging neighbouring pixels. Either way, resolution is lost by the factor $L$. Moreira et al. illustrate 2 × 2, 4 × 4 and 8 × 8 multilooking: interpretability improves greatly while detail is lost.

The equivalent number of looks (ENL) measures how much a processed image has been smoothed. It is computed over a homogeneous area as

$$\text{ENL} = \frac{\mathrm{E}[\hat f]^2}{\mathrm{Var}[\hat f]},$$

and for the original image it equals the nominal number of looks (Argenti et al., 2013). For intensity averaged over $L$ independent looks it follows from the variance $\sigma^2/L$ that the ENL is $L$. When looks overlap or neighbouring pixels are correlated, the ENL falls short of the nominal count; by our reading, this is why the Sentinel-1 table shows 4.4 for five range looks, which ESA lists with a look overlap of 0.25 (ESA, S1 Products).

Speckle filters estimate the reflectivity from local statistics instead of averaging blindly. Argenti et al. review their history. The local-statistics filter of Jong-Sen Lee (1980) is reportedly the first model-based despeckling filter. Frost’s filter weights a window with a kernel that depends on the local coefficient of variation, the ratio of local standard deviation to mean. Kuan’s filter implements the local linear minimum mean-square error (LMMSE) estimate exactly, combining each pixel with its local mean using weights set by the local signal-to-noise ratio; Lee’s filter is the same estimate up to a factor $(1+\sigma_u^2)^{-1}$, negligible for multilook images. Later methods include the gamma maximum a posteriori filter, wavelet-domain Bayesian estimators, and nonlocal methods such as the probabilistic patch-based filter and SAR-BM3D, which belong to the family of nonlocal filters that also includes non-local means. In the LMMSE estimate, by our derivation from the multiplicative model with $\mathrm{E}[u] = 1$ and $\mathrm{Var}[u] = C_u^2$, the filtered value is

$$\hat f = \bar g + k\,(g - \bar g), \qquad k = \frac{1 - C_u^2/C_g^2}{1 + C_u^2},$$

where $\bar g$ and $C_g$ are the local mean and coefficient of variation of the observed intensity $g$, and $C_u^2 = 1/L$ for $L$-look intensity. In a uniform area $C_g \approx C_u$ and $k \approx 0$, so the filter returns the local mean; near an edge or a bright target $C_g$ is large, $k$ approaches $1/(1+C_u^2)$, and more of the pixel’s departure from the local mean is kept: all of it for many looks, half of it for single-look data.

The script below simulates a 512 × 512 single-look scene with known reflectivity: a uniform field ($\sigma = 1$), a dark rectangle ($\sigma = 0.05$, a smooth surface such as calm water) and a bright line two pixels wide ($\sigma = 8$). It forms the complex image as circular Gaussian speckle scaled by $\sqrt{\sigma}$, then compares multilooking by block averaging, a 7 × 7 sliding mean (boxcar) and a 7 × 7 Kuan filter. For each it reports the ENL of intensity in a 160 × 160 uniform patch, the patch mean relative to the true $\sigma$ (a check for bias), and the line’s contrast: the peak of the column profile across it, divided by the background. A second part makes the speckle spatially correlated by keeping only the central half of the spectrum in each direction, so that the pixel spacing is half the resolution, as in an oversampled product. Seeds 0 to 4 are run and the minimum and maximum printed. The scene, metrics and filters were fixed before the first run. NumPy 2.3.5 and SciPy 1.16.3.

import numpy as np
from scipy.ndimage import uniform_filter

N = 512
sigma = np.ones((N, N))                 # reflectivity (mean intensity)
sigma[64:192, 320:448] = 0.05           # dark, smooth surface (e.g. calm water)
sigma[:, 256:258] = 8.0                 # bright 2-pixel line (e.g. a road edge)
patch = (slice(288, 448), slice(32, 192))   # homogeneous area, sigma = 1
rows, cols = slice(288, 448), slice(240, 273)

def slc(seed, band=1.0):
    """Single-look complex image: circular Gaussian speckle times sqrt(sigma).
    band < 1 keeps only |f| < band/2 cycles/pixel in both axes (oversampling)."""
    rng = np.random.default_rng(seed)
    z = np.sqrt(sigma / 2) * (rng.standard_normal((N, N))
                              + 1j * rng.standard_normal((N, N)))
    if band < 1.0:
        f = np.fft.fftfreq(N)
        keep = (np.abs(f)[:, None] < band / 2) & (np.abs(f)[None, :] < band / 2)
        z = np.fft.ifft2(np.fft.fft2(z) * keep) / np.sqrt(keep.mean())
    return z

def multilook(I, n):                    # average n x n blocks, then decimate
    return I.reshape(N // n, n, N // n, n).mean(axis=(1, 3))

def kuan(I, size=7, looks=1):           # local linear MMSE estimate
    m = uniform_filter(I, size)
    v = np.maximum(uniform_filter(I * I, size) - m * m, 0)
    cu2, cg2 = 1.0 / looks, v / np.maximum(m * m, 1e-12)
    k = np.clip((1 - cu2 / np.maximum(cg2, 1e-12)) / (1 + cu2), 0, 1)
    return m + k * (I - m)

def scaled(s, n):
    return slice(s.start // n, -(-s.stop // n))

def metrics(J, n=1):                    # n = decimation factor of J
    p = J[scaled(patch[0], n), scaled(patch[1], n)]
    profile = J[scaled(rows, n), scaled(cols, n)].mean(axis=0)
    return p.mean() ** 2 / p.var(), p.mean(), profile.max() / p.mean()

methods = {
    "single look":       lambda I: (I, 1),
    "multilook 2x2":     lambda I: (multilook(I, 2), 2),
    "multilook 4x4":     lambda I: (multilook(I, 4), 4),
    "multilook 8x8":     lambda I: (multilook(I, 8), 8),
    "7x7 boxcar":        lambda I: (uniform_filter(I, 7), 1),
    "7x7 Kuan filter":   lambda I: (kuan(I, 7), 1),
}
seeds = range(5)
res = {name: [] for name in methods}
cv_amp = []
for seed in seeds:
    z = slc(seed)
    I = np.abs(z) ** 2
    a = np.abs(z)[patch]
    cv_amp.append(a.std() / a.mean())
    for name, f in methods.items():
        res[name].append(metrics(*f(I)))

print("uncorrelated speckle, seeds 0-4 (min-max)")
print("single-look amplitude CV: %.3f-%.3f (Rayleigh: %.3f)"
      % (min(cv_amp), max(cv_amp), np.sqrt(4 / np.pi - 1)))
print("%-16s %7s %15s %15s %15s" % ("method", "pixels", "ENL", "mean / sigma",
                                    "line / backgr."))
for name, r in res.items():
    r = np.array(r)
    n = methods[name](np.zeros((N, N)))[0].shape[0]
    print("%-16s %4dx%-3d %6.2f-%-7.2f %6.3f-%-7.3f %6.2f-%-7.2f"
          % (name, n, n, r[:, 0].min(), r[:, 0].max(),
             r[:, 1].min(), r[:, 1].max(), r[:, 2].min(), r[:, 2].max()))

print("\nband-limited speckle (pixel spacing half the resolution), ENL")
for n in [1, 2, 4]:
    e = [metrics(multilook(np.abs(slc(s, band=0.5)) ** 2, n) if n > 1
                 else np.abs(slc(s, band=0.5)) ** 2, n)[0] for s in seeds]
    print("%dx%d looks (nominal %2d): ENL %.2f-%.2f" % (n, n, n * n, min(e), max(e)))

uncorrelated speckle, seeds 0-4 (min-max)
single-look amplitude CV: 0.522-0.525 (Rayleigh: 0.523)
method            pixels             ENL    mean / sigma  line / backgr.
single look       512x512   0.99-1.01     0.986-1.012     7.86-8.95   
multilook 2x2     256x256   3.96-4.10     0.986-1.012     7.64-8.43   
multilook 4x4     128x128  15.56-16.69    0.986-1.012     4.38-4.70   
multilook 8x8      64x64   61.74-72.15    0.986-1.012     2.68-2.83   
7x7 boxcar        512x512  47.45-53.11    0.986-1.011     2.96-3.10   
7x7 Kuan filter   512x512  36.48-40.84    0.987-1.011     4.42-5.12   

band-limited speckle (pixel spacing half the resolution), ENL
1x1 looks (nominal  1): ENL 0.99-1.01
2x2 looks (nominal  4): ENL 2.00-2.07
4x4 looks (nominal 16): ENL 5.90-6.58

The single-look amplitude has the coefficient of variation of a Rayleigh variable, $\sqrt{4/\pi - 1} \approx 0.52$, which follows from the Rayleigh moments, and the single-look intensity has an ENL of 1: on a uniform surface, the pixel-to-pixel fluctuation is as large as the signal. With independent speckle, block multilooking reaches its nominal number of looks, and every method leaves the mean unbiased to within the sampling error of the patch. The cost shows in the line. Up to 2 × 2 blocks it stays at its true contrast of 8, because the blocks happen to align with it; 4 × 4 and 8 × 8 blocks mix it with background and cut its contrast to about 4.5 and 2.7, and the 7 × 7 boxcar does the same without reducing the pixel count. The Kuan filter smooths the uniform patch somewhat less than the boxcar, about 37 to 41 looks against 47 to 53, but keeps 55 to 64 percent of the line’s contrast where the boxcar keeps under 40 percent, because its weight $k$ rises where the local coefficient of variation shows structure.

The second part shows why measured ENLs fall short of nominal looks. When the spectrum fills only half the band in each direction, neighbouring pixels share speckle, and averaging 2 × 2 or 4 × 4 of them gains only about half and about 40 percent of the nominal looks. The single-pixel statistics are unchanged; only the independence is lost. An ENL measured on a real product therefore reflects its oversampling and spectral weighting as well as its look count, which is the pattern in Sentinel-1’s table.

Geometric distortions

Because the radar measures range, not angle, the three-dimensional scene is projected onto slant range and azimuth, and sloped terrain is distorted (Moreira et al., 2013; Meyer, 2019). Meyer describes three effects:

• Foreshortening. A slope facing the sensor is compressed in the image, so a symmetric mountain appears to lean towards the radar. The effect depends on the look angle $\theta$ and the slope angle $\alpha$ and is largest as $\theta$ approaches $\alpha$.
• Layover. Where $\theta < \alpha$, the top of a slope is nearer to the radar than its base and is imaged in front of it; echoes from the slope overlap those from ground at the same range.
• Shadow. Areas behind steep slopes facing away from the radar cannot be seen by the sensor.

Larger look angles reduce foreshortening and layover but lengthen shadows, so the distortions cannot all be avoided with one geometry; images from more than one viewpoint, such as ascending and descending passes, may be needed (Meyer, 2019). In cities, layover mixes echoes from building walls, roofs and the ground in the same pixel, and Moreira et al. describe tomographic techniques used to separate them. For vision models, it follows that the same building looks different from opposite viewing directions, and that a SAR image cannot be overlaid on a map or an optical image without terrain-aware geocoding.

Wavelength, roughness and moisture

Backscatter depends on the surface’s geometry and roughness and on its electrical properties (permittivity), and microwaves can penetrate into the medium, more deeply at longer wavelengths, so that vegetation, ice, snow and dry soil act as volumes (Moreira et al., 2013). Moreira et al. tabulate the common bands: X-band (2.5 to 4 cm), C-band (4 to 8 cm), S-band (8 to 15 cm), L-band (15 to 30 cm) and P-band (60 to 120 cm), with L, C and X the most used. Meyer (2019) describes X-band signals as scattering mostly at the tops of tree canopies, while C- and L-band signals reach increasingly deep into the vegetation. ESA notes that most natural materials have a dielectric constant of 3 to 8 when dry and water about 80, so moisture in soil and vegetation raises reflectivity, and that smooth surfaces reflect the signal away from the radar and appear dark (ESA, S1 Mission). Oil on the sea appears dark for this reason: Moreira et al. explain that it damps the centimetre-scale capillary waves that would otherwise scatter the signal back.

Calibration

Radiometric calibration, described under Data It Produces, makes pixel values comparable between images and sensors. Geometric calibration, or geocoding, ties each pixel to a ground position (Moreira et al., 2013). It needs precise orbits and a terrain model, because range depends on height. Sentinel-1 GRD products are projected using a terrain height that varies only in azimuth (ESA, S1 Processing), so steep terrain is not fully corrected in them; radiometrically terrain-corrected backscatter needs separate processing, such as the gamma-nought Normalised Radar Backscatter product that ESA describes as a potential future Sentinel-1 core product, prototyped in an ESA activity (ESA, S1 Products). Sentinel-1 keeps its orbit within a tube of 60 m radius (RMS) around a reference path to support interferometry (ESA, S1 Mission).

Polarimetry and Interferometry

Polarimetry

A radar can transmit and receive in horizontal (H) or vertical (V) polarization. A fully polarimetric system measures the 2 × 2 complex scattering matrix $[S]$, with elements $S_{HH}$, $S_{HV}$, $S_{VH}$ and $S_{VV}$ (receive and transmit polarization), by alternating the transmitted polarization from pulse to pulse and receiving both (Moreira et al., 2013). In the usual monostatic case $S_{HV} = S_{VH}$, leaving five independent parameters once the absolute phase is ignored: three amplitudes and two relative phases. The scattering matrix describes a single deterministic scatterer; distributed targets need second-order statistics, a 3 × 3 coherency or covariance matrix averaged over several pixels. Decompositions split that matrix into scattering mechanisms. Moreira et al. describe the three-component decomposition proposed by Freeman and Durden in 1998, which models surface (Bragg) scattering, dihedral (double-bounce) reflection, as from a wall and the ground, and volume scattering from randomly oriented dipoles, as in a canopy. Sentinel-1 is a dual-polarization system: it transmits H or V and receives both, giving HH+HV or VV+VH, with VV+VH the main mode over land (ESA, S1 Mission). ESA notes that volume scatterers such as forest canopy have different polarization properties from surface scatterers such as the sea.

Interferometry

A single SAR image locates a scatterer in range and azimuth but not in elevation: everything on a circle around the flight path at the same range falls into the same pixel. Across-track interferometry (InSAR) adds a second image from a laterally displaced path (Moreira et al., 2013). For a perpendicular baseline $B_\perp$, a height difference $\Delta h$ changes the range difference by about $\Delta r \approx B_\perp \Delta h/(r_0 \sin\theta_i)$, measured as a phase difference

$$\Delta\varphi = \frac{2\pi m}{\lambda}\,\Delta r,$$

with $m = 1$ when one antenna transmits and both receive and $m = 2$ when each image has its own transmitter, as in repeat-pass acquisitions (Moreira et al., 2013). The processing chain is a vision pipeline in its own right: the two complex images are co-registered by maximizing their cross-correlation, the first is multiplied by the complex conjugate of the second to form the interferogram, the phase of a flat reference surface is subtracted, and the phase, known only modulo $2\pi$, is unwrapped and converted to height.

The quality of the phase is described by the interferometric coherence, the correlation between the two images. It is the product of losses from receiver noise, from temporal decorrelation (changes in the scene between acquisitions) and from geometric and volume effects (Moreira et al., 2013). Phase noise is reduced by averaging the complex interferogram over neighbouring pixels, again called multilooking, at the cost of resolution. Differential interferometry (DInSAR) removes the topographic phase with an elevation model, leaving a phase $4\pi\Delta r_\text{disp}/\lambda$ proportional to the displacement along the line of sight, measurable to a fraction of the wavelength; atmospheric delay and temporal decorrelation limit it (Moreira et al., 2013). Persistent scatterer interferometry follows stable point targets through long stacks of images to separate displacement from atmosphere (ESA, S1 Mission). Sentinel-1 synchronizes its TOPS bursts between repeat passes to make interferometry possible (ESA, S1 Mission).

Processing the Data

A typical chain for amplitude-based work, assembled from the steps described above, is calibration to $\sigma^0$ or $\gamma$, thermal noise removal, multilooking or speckle filtering, terrain correction and geocoding, and conversion to decibels. Each choice matters for learning (our reasoning):

• Statistics. Speckled intensity is exponential or gamma distributed, heavy-tailed and signal-dependent. A loss or normalization designed for additive Gaussian image noise is mismatched to it, and, as Argenti et al. point out, an estimate made after the log transform is biased, since the mean of $\log u$ is not zero.
• Filtering. Image denoising methods and speckle filters trade ENL against detail. Argenti et al. warn that despeckling should preserve the local mean of backscatter, point targets, linear features and textures, and they assess filters on homogeneous areas by ENL and elsewhere by the ratio of the noisy to the filtered image, which should look like pure speckle if no structure was removed.
• Geometry. Slant-range images are not maps. Labels from optical images or maps must be brought into radar geometry, or the SAR image geocoded with a terrain model, before pixels correspond; layover and shadow areas carry no reliable labels.
• Phase. Most learned models use amplitude only. Complex SLC data, polarimetric matrices and interferometric coherence are additional inputs, and they require the co-registration and conventions of the products they come from.

Missions

Spaceborne SAR began with Seasat, launched by NASA in 1978. Moreira et al. describe it as the first civilian SAR satellite: L-band, HH polarization, operating for only about three months. Europe’s ERS-1/2, Japan’s JERS-1 and Canada’s Radarsat-1 followed in the 1990s, and TerraSAR-X, TanDEM-X, COSMO-SkyMed and Radarsat-2 introduced resolutions of about a metre from 2007 (Moreira et al., 2013). The public missions most used in research today, as their operators describe them as of October 2026:

Mission	Operator	Launches	Band and wavelength	Resolution and swath	Repeat
Sentinel-1	ESA, for the EU’s Copernicus	1A: 3 Apr 2014; 1B: 25 Apr 2016; 1C: 5 Dec 2024; 1D: 4 Nov 2025	C-band, 5.405 GHz (about 5.55 cm)	IW: 5 × 20 m single look, 250 km swath; SM and WV: about 5 × 5 m; EW: 20 × 40 m, 400 km	12 days per satellite, 6 days with two
NISAR	NASA and ISRO	30 Jul 2025	L-band (24 cm) and S-band (9.4 cm)	3 to 10 m, depending on mode	12 days; about 6 days on average with ascending and descending passes
ALOS-2 and ALOS-4	JAXA	ALOS-2: 24 May 2014; ALOS-4: 1 Jul 2024	L-band	ALOS-4: stripmap 3, 6 or 10 m over 100 to 200 km; ScanSAR 25 m over 700 km; spotlight 1 × 3 m	—

Sentinel-1. ESA describes Sentinel-1 as two sun-synchronous satellites in the same orbital plane, phased 180° apart, at an altitude of 693 km (ESA, S1 Mission). The instrument’s antenna is 12.3 m by 0.821 m, its bandwidth is programmable up to 100 MHz and its PRF from 1,000 to 3,000 Hz. It has four exclusive modes, of which IW, with VV+VH polarization, is the main mode over land and Wave mode the default over the open ocean. After Sentinel-1B’s mission ended in 2022, as Remote Sensing describes, Sentinel-1C joined Sentinel-1A. In April 2026, ESA announced that Sentinel-1D data would open to users that month, that Sentinel-1C would be manoeuvred in the second half of June to re-establish a six-day revisit with Sentinel-1D, and that Sentinel-1A operations would be phased out once that transition, expected in early July 2026, was complete (Copernicus Sentinel Online, 2026). The new pair’s orbit shifts the six-day revisit pattern by one day relative to the A/B pair (ESA, S1 Mission). As of October 2026, the SentiWiki mission page still gives the end of Sentinel-1A operations as planned for the end of June 2026; we did not find an operator statement confirming when it ended. Sentinel data are free, full and open under EU law, as Remote Sensing describes.

NISAR. The NASA–ISRO SAR mission was launched on 30 July 2025 from the Satish Dhawan Space Centre on an ISRO GSLV Mark II rocket. NASA lists a 747 km orbit, a 12-day exact repeat, left-looking geometry, a baseline mission of three years, and free and open data, with L-band data archived at the Alaska Satellite Facility and S-band data distributed by ISRO. NASA reports that provisional, fully calibrated L-band products were released on 20 July 2026 (NASA, NISAR).

ALOS-4. JAXA’s ALOS-4 carries PALSAR-3, a phased-array L-band SAR that succeeds PALSAR-2 on ALOS-2. JAXA’s page compares the two: the stripmap swath widens from 50 or 70 km on ALOS-2 to 100 to 200 km on ALOS-4 at the same resolutions, and the planned frequency of stripmap observations over Japan rises from four to twenty times a year (JAXA, ALOS-4). JAXA’s launch records give the launch of ALOS-4 on an H3 rocket on 1 July 2024 and of ALOS-2 on 24 May 2014.

History. Moreira et al. trace the principle to Carl Wiley’s invention of 1951, followed by a patent application in 1954, which used a coherent radar and Doppler beam sharpening to overcome the azimuth resolution of side-looking radar. Meyer (2019) dates Wiley’s discovery, made at Goodyear Aircraft, to 1952.

Strengths

• Independent of light and weather, which suits regular monitoring and disaster response (Moreira et al., 2013).
• Azimuth resolution independent of range, the same from an aircraft or from orbit.
• Physical and coherent measurements: calibrated backscatter responds to roughness, structure and moisture, and phase supports polarimetry and interferometry.
• Systematic archives: missions such as Sentinel-1 revisit the same areas with the same geometry on a fixed schedule.

Limitations

• Speckle: single-look images have an ENL of one, and reducing speckle costs resolution or detail.
• Geometry: slant-range projection, foreshortening, layover and shadow hinder interpretation and alignment with maps.
• Sensor dependence: brightness changes with wavelength, polarization and incidence angle, so models trained on one sensor or mode may not transfer, and labels often have to come from optical data or maps (our reasoning).
• Design trade-offs: swath and azimuth resolution conflict in single-channel systems (Moreira et al., 2013).

Typical Applications

The applications that ESA lists for Sentinel-1 include land, sea-ice and land-ice monitoring, marine monitoring and maritime surveillance, and emergency response (ESA, S1 Mission). Polarimetric data serve crop-type identification and soil moisture, forest biomass and fire scars, wetland and snow monitoring, sea-ice identification, oil-spill detection, and ship detection and classification; interferometry serves hazard monitoring for earthquakes, volcanoes and landslides, subsidence, glacier motion and elevation mapping (ESA, S1 Mission). For vision, these become familiar tasks on unfamiliar data: object detection of ships against sea clutter, semantic segmentation of floods, oil slicks and sea ice, land-cover classification, and change detection between repeat passes, where the stable geometry and the coherence between acquisitions help.

Comparison with Other Sensors

• Optical and multispectral imagers are passive, measure reflected sunlight in many bands and produce images in angular geometry that people interpret easily, but they need daylight and clear skies. SAR measures one band’s backscatter, with phase, in range geometry, regardless of weather; the two are often fused, which Remote Sensing names as a research problem of its own.
• Laser scanning. LiDAR is also active and ranging, but at optical wavelengths, which fog and rain degrade; it resolves angle with a narrow beam and returns a sparse point cloud, where SAR resolves azimuth by synthesis and returns a dense image with speckle.
• Tomography. Computed tomography is the closest relative in one respect: both images are computed from measurements by an inverse problem whose sampling decides which artifacts appear.