Fig. 1. Schematic representations of different approaches for generating synthetic wavelengths.

Fig. 2. (a) Adjusting the synthetic wavelength between 10 and 1250 mm in four steps requires radio frequencies in the range of 24 to 30 GHz. (b) Temporally varying frequencies ν of laser light and sidebands ν0+f1,2 generated by a radio-frequency-controlled frequency shifter. Interferograms at ν0+f1,2 are recorded during Tm1,2, whereas Ts represents the switching time for changing the radio frequency from f1 to f2. The synthetic frequency F may differ from the exact value f2−f1.

Fig. 3. Schematic setup of the synthetic-wavelength generator comprising a near-infrared (NIR) laser single-sideband modulator driven at the radio frequency f, an erbium-doped amplifier (EDFA), and a frequency doubler (SHG). The NIR output serves for spectral characterization, whereas the VIS output is connected to a powermeter.

Fig. 4. (a) Optical output spectrum in the near-infrared when the modulator is driven with a 10 GHz radio-frequency signal. (b) Temporal evolution of the normalized power in the spectral components at ν+Nf with N=−2,…,+2, measured over a period of 24 h.

Fig. 5. Measured frequency shift in the near-infrared and corresponding values in the visible as a function of time. (a) Temporal evolution of the frequency shift resembles the contour of the ruins of Hochburg Emmendingen, located near Freiburg, Germany. (b) A 1-s zoom-in of the trace highlights characteristic features. Selected frequency shifts are annotated with their corresponding values in terms of the respective synthetic wavelengths Λ.

Fig. 6. Setup for holographic measurement. The synthetic-wavelength generator is connected to the interferometer via the 780-nm-wavelength port. A connected computer receives the images from the camera for computing the phase maps and sets the bias voltages of the single-sideband modulator and the desired microwave frequencies f for the corresponding synthetic wavelength Λ.

Fig. 7. (a) Photograph of the machine-milled sample with nominal height values. (b)–(d) Interferometrically determined surface shapes using one (b), two (c), and three (d) synthetic wavelengths. Here, the height values are means and respective standard deviations over 200pixel×200pixel subsections.

Fig. 8. (a) Output spectra of the single-sideband modulator for different DC voltage combinations. The carrier extinction ratio (CER) as well as the sideband extinction ratio (SER) can be varied almost independently. (b) Height values for different values of CER and SER. The values highlighted with an asterisk have been determined by the respective spectra in panel (a).

Fig. 9. (a) Photograph of the brick sample with nominal height values. (b, (c) Interferometrically determined surface shapes using one (b) and two (c) synthetic wavelengths. Here, the height values are means and respective standard deviations over 200pixel×200pixel subsections.