## 1 Introduction  
Confocal microscopes [1; 2] are valuable instruments for non-contact surface profile measurement [3; 4], and are employed in various scientific and industrial fields due to their principles that allow three-dimensional profile measurement in the ambient atmosphere. One of the main features of the confocal probe employed in a confocal microscope is a depth-sectioning effect that realizes a high resolution measurement in the axial direction by extracting a signal from the focal plane while excluding the unnecessary signals from the other planes [5]. In the case of a confocal probe employing a monochromatic light source [6; 7; 8; 9], it is necessary to scan a target sample in the axial direction for obtaining an axial response; the maximum signal of the axial response is reached when the surface is exactly located on the focal plane of the objective lens in the confocal probe [9]. Meanwhile, in the case of a confocal probe employing a chromatic light source and a chromatic objective lens, which is often referred to as the chromatic confocal probe [9; 10; 11; 12], the height information can be obtained by monitoring the light spectrum detected by the point detector in the confocal probe. In a chromatic confocal probe, the axial chromatism is used as a space-coding method, in which a different wavelength is associated with each point of the optical axis to provide a mathematical relationship between the surface height and the wavelength focused on the surface [9]; namely, the height information can be obtained without scanning the target in the axial direction. This characteristic allows the chromatic confocal probe to reduce the influences of motion errors of the mechanical scan of a target sample. Conventional chromatic confocal probes employing a white light source such as a halogen lamp or an LED (light-emitting diode) have been achieved a sub-micrometric vertical resolution [13; 14; 15; 16]. Meanwhile, instability and low spectral power density of such a white light source are issues to be addressed to achieve better performances. In responding to the background described above, several types of chromatic confocal probes employing a super-continuum light source, which has a higher light intensity, better spatial coherence, and a wider spectral range, have been developed so far [17; 18; 19; 20]. In addition, optical configurations with various dual-detector setups have been proposed to obtain axial responses in a better sensitivity [21; 22; 23; 24]. The author's group has also proposed a chromatic confocal probe with a new dual-detector setup and a mode-locked femtosecond laser source [24]. The proposed femtosecond laser chromatic confocal probe is designed to divide the reflected laser beam from a target sample surface into two beams and capture them by two identical fiber detectors of an optical spectrum analyzer. It should be noted that one of the divided beams is coupled into the fiber detector placed on the focal plane of a coupling lens, while the other beam is coupled into another fiber detector placed on the plane slightly shifted from the focal plane of another coupling lens; namely, the optical setup has two different confocal setups. By obtaining light spectra of the divided beams captured in the different confocal setups, the \"normalized\" spectrum, which can be employed as a highly-sensitive axial response, can be obtained [24]. Experimental results have demonstrated that the proposed method can realize a vertical resolution of 30 nm and a measurement range of 40 \(\upmu\)m [24]. Furthermore, it has also been demonstrated that the measurement range can be expanded to 250 \(\upmu\)m by utilizing side-lobes in the normalized spectrum [25]. On the other hand, since an optical spectrum analyzer is employed to read the spectra over a wide light wavelength range of 160 nm in the developed setup, it takes a relatively long time (8 s) to make the measurement at one height position of a target sample.