Stroboscopic scanning white light interferometry (SSWLI) allows precise three dimensional (3D) measurements of oscillating samples. Commercial SSWLI devices feature limited pulsing frequency. To address this issue we built a 400-620 nm wideband 150 mW light source whose 1.6 µm wide interferogram is without side peaks. The source combines a non-phosphor white LED with a cyan LED. We measured a calibration artifact with 10 nm precision and obtained 40 nm precision when measuring the 3D profile of a capacitive micromachined ultrasonic transducer membrane operating at 2.72 MHz. This source is compatible with solid state technology.
© 2013 OSA
It is possible to do fast stroboscopic imaging [1–3], but it is hard to precisely image rapidly moving structures [1,4]. For microelectromechanical systems/nanoelectromechanical systems (MEMS/NEMS) it is desirable to reach nm precision with structures that oscillate at several MHz [1,3]. To be able to do this new light sources are needed.
Light emitting diodes (LEDs) are replacing halogen bulbs as light sources for scanning white light interferometry (SWLI). LEDs offer long lifetime, low heat generation and compact size. In addition they can be rapidly pulsed. This allows stroboscopic measurements of samples oscillating at a few MHz [1,2,5].
For precise measurements phosphor-based white LEDs are preferred  rather than single color LEDs which feature long coherence length. Phosphor-based sources suffer from two drawbacks: 1, their non-Gaussian output spectrum featuring two peaks causes interferogram ringing which may degrade the precision along the z-direction ; 2, phosphorescence which makes their switching time longer than that of solid state single color LEDs [1,7,8]. Consequently for high frequency stroboscopic measurements narrow band single color LEDs have to be used [1,3]. Wide emission bandwidth in a rapidly switchable source can be achieved by combining several single color LEDs, but this increases the complexity of the light source.
Non-phosphor white LEDs can be manufactured using different methods. Common methods produce light sources emitting in the yellow and blue parts of the visible spectrum [9,10]. For instance one can stack quantum wells (Qwells) that emit different wavelengths . The Qwells feature a certain thickness or chemical composition that results in a specific emitted wavelength. By choosing layers with suitable specifications (thickness, doping etc) emitting blue and yellow white emission could be achieved. One can also create indium rich quantum dots that emit yellow light into a blue emitting InGaN layer . This also results in white emission.
A disadvantage of these current non-phosphor white LEDs is their two-peak emission spectrum which causes similar interferogram ringing as seen with phosphor LEDs. The interferogram ringing could in principle be reduced by combining the white non-phosphor LED with a cyan LED. A similar kind of hybrid source was built using a phosphor white LED . A hybrid non-phosphor LED should feature an interferogram without side peaks and it should permit rapid pulsing.
We set out to construct a non-phosphor white LED [9,10,12] source allowing fast switching and having a wide bandwidth. Our contribution is to realize that by changing the phosphor LED in the setup of Wan et al  for a non-phosphor one we get what we want.
2.1 Building the light source
When building the hybrid light source the most important issue is to select the central wave length of the cyan LED to fit the gap in the emission spectrum of the non-phosphor LED. We used one non-phosphor white LED (L-513NPWC-15D, American Opto Plus) and one cyan LED (Everlight EL-333-2UBGC/S400-A4) whose mean wavelength is 504 nm and full width half maximum (FWHM) is 34.1 nm. Light from the LEDs is combined using a beam splitter (Edmund Optics NT46-669), Fig. 1 . This produces uniform illumination featuring the combined spectrum of the LEDs. The spectrum of the hybrid source can be controlled by changing the input current to the LEDs.
Stroboscopic interferometry requires synchronized light pulses shorter than 10% of the sample oscillation period to avoid blurring caused by sample motion . Usually this reduces the effective light power of the source, leading to a low signal to noise ratio. Fortunately LEDs can briefly be operated above their nominal drive current . We drive the LEDs with custom-built pulsers, Fig. 2 , that can create 6.2 ns current pulses with peak currents exceeding 5 A. This provides similar intensity as that obtained with these LEDs working in DC mode using specified drive currents 20 mA (cyan) and 30 mA (white). The LED pulser is controlled by the same signal generator that drives the sample. The cyan light responds slightly faster to the voltage pulses of the pulser. Thus we added a delay line to the cyan LED to make the light pulses of the LEDs simultaneous. In the measurements at 2.72 MHz we used a 9.15 m long coaxial cable (Bedea, RG175) providing a time delay of 46 ns.
2.2 Modeling of interferograms in the static situation
To choose the cyan LED specimen and operating characteristics (drive currents) we modeled the interferograms created by the source in a static situation . As the source emission spectrum is non-Gaussian, modeling the interferograms is necessary both to predict the width of the interferogram and to estimate the side peak level.
Here g is the interference at a certain position and V is the source spectrum
In this expression h is the height of the measured point of the sample whereas φ0 is the phase difference between the two arms of the interferometer. Because the numerical aperture of the objective is small (0.13) the beam angle is assumed to be low and to have negligible effect on the interference.
First we simulated interferograms by mathematically combining the specified emission spectra of different LEDs and the non-phosphor LED. This allowed us to identify a suitable LED to fill the gap in the spectrum of the non-phosphor LED. Next we measured the combined emission spectrum of the hybrid source at different operating currents using a calibrated spectrometer (Ocean optics, HR 2000 + ). We finally identified the preferred operating currents by simulating interferograms based on these spectra.
2.3 SWLI measurements
These tests were carried out to prove that the hybrid source advances the state of the art of stroboscopic scanning white light interferometry (SSWLI). The SWLI measurements were done using a setup comprising the hybrid light source, a Nikon 5x Michelson type interferometric objective, a 0.6x tube lens, and a Pulnix TM-6740GE CCD camera (Fig. 1). Our pixel size was 2.47 μm. A piezoelectric actuator (PI, P-723.10) provided 100 μm measurement range . In a SWLI measurement the sample-objective distance is scanned using a piezo actuator. Images are taken every 68 nm of the scan (1/8 of the mean wavelength emitted by the light source). The position where the sample-to-beam splitter and the reference mirror-to-beam splitter distances are equal is calculated for each pixel based on the locally detected interference . In SSWLI measurements the sample motion is “frozen” using pulsed light, in all other aspects they are similar to normal SWLI measurements. The phase shift between the LED pulsers and the sample actuation was controlled by introducing a delay between the two channels of the function generator (Tektronix, AFG3252) .
First we tested the hybrid source by measuring the step height of a gold plated MEMS sample and a calibration artifact (VSLI, 1800CQ). This was to ensure that the measurement precision of our system is not reduced by the new source. The results were compared to ones acquired using a standard halogen light source (Philips 6958). To test the stroboscopic measurement capability we measured dynamic 3D profiles of a capacitive micromachined ultrasonic transducer (CMUT) oscillating at 2.72 MHz frequency [4,18]. We compared the recorded motion to that obtained with a laser Doppler vibrometer (LDV) (Polytec OFV 3001).
3.1 Pulsing characteristics
The light pulses are short enough for SSWLI. To test the pulsing characteristics of the LEDs we first measured the output current of the pulser. Then we measured the light output of LEDs using a photodetector (Antel AFM-S). The rise/fall time of the detector is 1.2 ns (bandwidth 300 MHz). The full duration at half maximum (FDHM) of the electric pulses was 6.21 ± 0.10 ns and the peak current was 5.00 ± 0.15 A, Fig. 3 . The shortest measured light pulses were 8.42 ± 0.10 ns (FDHM) using non-phosphor white LEDs and 6.36 ± 0.10 ns using cyan LEDs (Fig. 3, Table 1 ). These data predict that stroboscopic measurements at 15.7 MHz using the cyan LED and 11.9 MHz using both LEDs should be possible (these numbers correspond to 10% duty cycle).
3.2 Spectral measurements and simulated interference of hybrid source
The hybrid source produces the predicted emission spectrum (central wavelength and FWHM of the interferogram). The spectrum of the non-phosphor LED changed at high pulsing frequencies, Fig. 4 , compared to that recorded at low pulse repetition rates. According to our simulations this alters the central wavelength and FWHM of the shortest possible interferograms without side peaks only slightly (0.13 µm). Based on the simulations we should be able to produce interferograms with a FWHM of 1.44 µm when driving the LEDs with DC, whereas at 3 MHz interferograms with 1.57 µm FWHM and no side peaks should be achievable. With some pulsing frequencies the shortest possible simulated interferogram was shorter than that obtained with DC (e.g. 1.43 µm at 1.2 MHz).
3.3 Stroboscopic SWLI measurements
Our static calibration measurements showed no imaging distortion. Measurements on a 7 µm tall gold plated step sample show that the measurement precision of our SWLI setup is unaffected by the new light source (Table 1). The measured step height was 6.96 ± 0.03 µm which is comparable to the result obtained using a halogen lamp 7.025 ± 0.020 µm. We also validated the instrument using a step height standard specified to be 185.3 ± 0.23 nm which compares well with the measured height, 181 ± 5 nm (Fig. 5 ). Measurements on the zoom box calibration standard revealed that this precision was maintained across a 1.1 um by 1.3 um aperture (Fig. 5).
From the interferograms extracted from the measurement data one sees 1.66 ± 0.04 µm wide interferograms without side peaks, Fig. 6 , using the light source driven at 2.72 MHz frequency and 5% duty cycle. This is close to the narrowest interferograms (1.445 ± 0.007 µm) without side peaks that were simulated based on the spectra emitted by the two LED sources driven at DC. The simulation also took into account the impact of the instrument.
We measured the spectrum of the hybrid source using 2.72 MHz and 5% duty cycle while performing the step measurements (Fig. 6). The interferogram simulated based on this spectrum and the spectral response of the camera was similar to the measured one: 1.6 µm FWHM (Fig. 6).
We measure dynamic 3D profiles of CMUT transducers operating at 2.72 MHz frequency. The CMUTs were biased by 30 V DC (collapse voltage is approximately 50 V) and were actuated by 5 Vpp sinusoidal signal. We determined the vibration amplitude to be 430 ± 40 nm in the middle of the moving elements while the stationary parts between the elements remained relatively still (height variation below measurement precision) (Fig. 7 ).
These results compare well with laser vibrometer data. Based on the LDV results the frequency is 2.72 MHz and the displacement exceeds the measurement range, 150 nm, at the center of the moving CMUT elements. The area that can’t be measured with the LDV has a deflection amplitude exceeding 150 nm based on the SSWLI measurements. Closer to the edges the measured displacements agree. We fitted a sine to both SWLI (24 measurements at 30 degree phase shift between each) and LDV measurements (span over several cycles) at 6 points where the peak-to-peak movement measured using LDV was 20-140 nm. The precision for the sine fits (95% confidence interval) was 17.6 nm or better for the SWLI and 0.29 nm or better for the LDV (single point measurement). The difference between the amplitudes measured with SWLI and LDV in these points was 10 ± 20 nm.
Figures 6 and 7 show our main results. As far as we understand there should be very little possibility for artifacts due to our validation work. Hence it is safe to claim that we have achieved 2.72 MHz at 1.6 um coherence in a real measurement. Moreover, Fig. 3 indicates that we should be able to image at least up to 11 MHz oscillatory motion. Our result advances the state of the art as represented by the Veeco currently Bruker device  because we use white light at high frequencies. This means that we are not restricted to the lambda/4 problems of phase shifting interferometry.
The implication of this work is that we have broadened the field of applicability of white light interferometry. It is also important to realize that this phosphorless solution allows us to use all the benefits that solid state technology brings with it.
There is one issue that needs to be discussed regarding measuring rapidly moving samples. As seen in Fig. 4 the coherence length depends on the applied current, on its amplitude, frequency, and duty cycle. This means that the precision of the surface imaging is not constant. For instance Hutchins  showed that there may be as much as 2% difference in z-coordinate when measuring a bending membrane using CW and pulsed light (red LED).
The source spectrum is compromise between the short coherence length of the phosphor LED and the narrow but single peaked spectrum of a normal LED. A wider spectrum could be achieved by using more LEDs. Such a setup could also potentially permit more precise tailoring of the coherence function  even at fast switching rates across a wide region of wave lengths.
We measured dynamic 3D profiles of a CMUT device oscillating at 2.72 MHz. This frequency is higher than what has been reported previously with a SSWLI device [2,3]. The precision of the amplitude measurement was 40 nm.
Pulses with 6.36 ns FDHM were created using the cyan LED and pulses with 8.42 ns width were created using both LEDs in the hybrid source. This means that oscillations exceeding 11 MHz should be measurable.
The wide continuous spectrum needed for SWLI measurements can be produced by combining a non-phosphor white LED with a single color Cyan LED. Interferograms with a FWHM as low as 1.6 µm were produced without side peaks. Our solution is compatible with solid state technology.
We thank Professor Mario Kupnik, Brandenburg Technical University, GER for the CMUT sample. We also acknowledge the help of Mr. Ben Wälchli and Ph.L. Juha Aaltonen with the measurement setups. This work was supported by Academy of Finland Photonics and modern imaging techniques program projects 134915 and 134895.
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