If a SAR image pixel has a value b+ai, its phase ɸ is given by _______ sin-1(a/b) sin-1(b/a) tan-1(b/a) tan-1(a/b)

To determine the phase $\phi$ of a pixel with a value $b + ai$ in synthetic aperture radar (SAR) imaging, we should consider the relationship between the real part $b$ and the imaginary part $a$.

Step 1: Break Down the Problem

We need to find out how to express the phase $\phi$ using the components $a$ and $b$ of the complex number $b + ai$. The phase can typically be calculated using the arctangent function, which gives the angle corresponding to the ratio of the imaginary part to the real part.

Step 2: Relevant Concepts

The phase $\phi$ of a complex number $z = x + yi$ can be defined as: $\phi = \tan^{-1} \left( \frac{y}{x} \right)$ where $x$ is the real part and $y$ is the imaginary part.

Step 3: Analysis and Detail

For $z = b + ai$:

• Here, $b$ corresponds to the real part $x$.
• $a$ corresponds to the imaginary part $y$.

Thus, we use: $\phi = \tan^{-1} \left( \frac{a}{b} \right)$ As we can see, the required expression for phase is based on the ratio of the imaginary component over the real component.

Step 4: Verify and Summarize

From our analysis, the correct expression for the phase $\phi$ in this context is $\tan^{-1}(a/b)$. The other options given (e.g., sin-inverse functions) are not relevant for determining the phase of a complex number.

Final Answer

The phase $\phi$ is given by $\tan^{-1}(a/b)$.