An optical measurement system for measuring an optical fiber sensor (3, 24) including multiple optical cores, the system comprising: a tunable laser (1, 16) configured to sweep laser light over a measurement range of wavelengths; an optical amplifier connected to an output of a pump laser, the optical amplifier configured to amplify the swept laser light; an optical network (2, 12) configured to provide the amplified swept laser light to the multiple optical cores, and to output optical signals comprising reflected light from the multiple optical cores; detection and acquisition circuitry (4, 20) configured to convert the optical signals into electrical signals associated with the multiple optical cores; and data processing circuitry (5, 22) configured to process the electrical signals to determine strains in the multiple optical cores, wherein the detection and acquisition circuitry or the data processing circuitry is further configured to: control the tunable laser to sweep the laser light over the measurement range of wavelengths in rising and falling sweeps, and control a gain of the optical amplifier by adjusting a power of the pump laser to at least one of: balance a power of the amplified swept laser light between the rising and falling sweeps, balance the power of the amplified swept laser light between different wavelengths during the rising sweeps, or balance the power of the amplified swept laser light between different wavelengths during the falling sweeps. a tunable laser (1, 16) configured to sweep laser light over a measurement range of wavelengths; an optical amplifier connected to an output of a pump laser, the optical amplifier configured to amplify the swept laser light; an optical network (2, 12) configured to provide the amplified swept laser light to the multiple optical cores, and to output optical signals comprising reflected light from the multiple optical cores; detection and acquisition circuitry (4, 20) configured to convert the optical signals into electrical signals associated with the multiple optical cores; and data processing circuitry (5, 22) configured to process the electrical signals to determine strains in the multiple optical cores, wherein the detection and acquisition circuitry or the data processing circuitry is further configured to: control the tunable laser to sweep the laser light over the measurement range of wavelengths in rising and falling sweeps, and control a gain of the optical amplifier by adjusting a power of the pump laser to at least one of: balance a power of the amplified swept laser light between the rising and falling sweeps, balance the power of the amplified swept laser light between different wavelengths during the rising sweeps, or balance the power of the amplified swept laser light between different wavelengths during the falling sweeps. control the tunable laser to sweep the laser light over the measurement range of wavelengths in rising and falling sweeps, and control a gain of the optical amplifier by adjusting a power of the pump laser to at least one of: balance a power of the amplified swept laser light between the rising and falling sweeps, balance the power of the amplified swept laser light between different wavelengths during the rising sweeps, or balance the power of the amplified swept laser light between different wavelengths during the falling sweeps.