The method used to manufacture a Young’s double pinhole interferometer is discussed. This interferometer is destined to be used in a surface profilometer using two wavelengths so that the zero order fringe can be determined. Hence stringent requirements are placed on the absolute length difference between the two output fibers of a single mode coupler. These requirements are discussed along with the manufacturing process. The interferometer is shown along with measurements showing a length difference on the order of 6µm.
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where Io is the initial power out of one fiber (pinhole), 2a is the fiber separation, k=2π/λ, λ is the wavelength, and Δϕ is the phase difference of the light at a plane immediately in front of the fibers.
As long as Δϕ is constant, the location of the zero order fringe (corresponding to x=0) will be independent of wavelength. However, if the fibers from the coupler to the “pinholes” differ in length, or if the fiber endfaces are not perfectly aligned, then Δϕ will be wavelength dependent since
is the effective refractive index of the fiber core, Δn
) is the change in refractive index due to dispersion, no
is the refractive index of air, λ1
are the two wavelengths used to calculate the zero order fringe, and d
is the offset between the two fibers endfaces illustrated in Figure 1
2 Fringe Generator Requirements
The two requirements on the fringe generator (or pinholes) are good fringe visibility and zero order fringe stability at both wavelengths of operation. The wavelengths being used for this system are 633nm (HeNe) and 830nm, primarily because sources and detectors at these wavelengths are readily available at a low cost.
To achieve good fringe visibility, the fiber coupler needs to be approximately a 3dB coupler, which splits the light approximately 50/50 between the two output fibers. To achieve zero order fringe stability at both wavelengths, we need to ensure that the phase difference expressed in Eq. (2)
is small. We established a criterion that the phase difference, Δϕ
, must be less than 2π
/30, which will ensure that the fringes move less than one pixel when imaged by the CCD camera.
Looking again at Eq. (2)
, if dispersion is neglected (Δn
=0), any small length difference could be easily compensated for by adjusting the offset between the fiber endfaces so that d
. We note that d
must still be less than 0.5mm so that the light diverging from the short fiber endface does not intersect the long fiber. If we include the effects of dispersion and adjust the fiber offset as described, then Eq. (2)
is greatly simplified and we can determine the maximum fiber length difference as
Using Ref. [4
4. Optical Society of America, Handbook of Optics,W. G. Driscoll, ed. (McGraw-Hill, New York, 1978).
, pg. 7–85, Table 16], Δn
was determined to be 4.2×10-3
. Thus, the maximum fiber length difference we can tolerate is 6.6µ
3 Manufacturing Process
A fiber coupler designed to have a 50/50 splitting ratio at both 633nm and 830nm is not a commercial-off-the-shelf item. Hence the first step in manufacturing this fringe generator was to make a coupler with the proper splitting ratio. The process for fabricating a thermally fused biconical tapered coupler is well described in [5
5. Z. G. Wang, Wavelength compensation in fused fiber couplers, Ph.D. Disseration, (Virginia Polytechnic Institute and State University, Blacksburg, VA, 1996).
]. Briefly, however, two fibers are connected to the two sources. A small section of the fibers are stripped of their jacket and buffer, and twisted together. Using a propane torch, the fibers are then heated and pulled so that they are tapered and fused together. The power out of each fiber is monitored in real time so that the tapering process can be stopped when the splitting ratio is approximately 50/50. Our coupler manufacturing station is shown in Figure 2
Schematic of the fiber alignment used to compute the optical path difference using Eq. (2)
is the length of the long fiber, L
is the length of the short fiber, d
is the normal distance between two lines parallel to the fiber endfaces, ϕ
is the phase of the light exiting the long fiber, ϕ′
is the phase exiting the short fiber and ϕ
is the phase of the short fiber’s light when it is parallel to the long fiber endface.
Fig. 2. The coupler manufacturing station used to make the coupler in this system.
To ensure the fibers are equal lengths, within a few microns, a white light interferometer is used, as shown in Figure 3
. This is essentially a fiber optic Michelson interferometer with a broad spectrum superluminescent light emitting diode (SLED) source to inject light into the coupler [6
6. T. Li, A. Wang, K. Murphy, and R. Claus, “White-Light Scanning Fiber Michelson Interferometer for Absolute Position-Distance Measurement,” Opt. Lett. 20, 785–787 (1995). [CrossRef] [PubMed]
]. The back reflections are then observed by an Ando optical spectrum analyzer. Fringes will develop on this spectrum corresponding to the path difference, which can be measured using:
are the wavelengths of any two adjacent peaks of the fringe pattern on the spectrum. In our setup, the two post-coupler fibers are cut so that one is approximately 1mm longer than the other. The two fibers are then mounted onto a polishing machine so that the pressure of each fiber against the lap can be controlled (see Figure 4
). The white light interferometer is then used to measure the length difference while the longer fiber is polished.
Two spectra obtained during polishing are shown in Figure 5
. Figure 5
(a) is the initial spectrum which shows a fringe separation of 0.2nm. This is converted to a fiber length difference using Eq. (4)
. Doing so yields a length difference of approximately 1mm, which agreed with what we observed by pulling the two fibers taut. A spectrum mid-way through the polishing process is shown in Figure 5
(b). The fringe separation has increased to approximately 1nm and the length difference decreased to 230µ
Fig. 3. The fiber length difference is measured using a white light interferometer.
Fig. 4. The fibers are mounted onto the polishing machine so that the pressure of each fiber against the lap can be controlled. Polishing continues until the desired length difference is achieved.
Fig. 5. Sample spectra obtained during the fringe generator manufacturing process. (a) The initial spectrum which shows a fiber length difference of approximately 1mm. (b) A spectrum mid-way through the process; the length difference has decreased to 230µm.
A comparison of the final spectrum (red) and initial spectrum (blue) taken at the same time as Figure 5
(a). The fringes readily observed are noise arising from some other reflection in the system.
A low-pass filtered version of a spectra in Figure 6
Given the limitation of the SLED spectrum width, we could not reliably measure length differences smaller than 6µ
m. Hence continuing to polish the fibers would not be useful, especially since the length difference meets the requirement discussed in Section 2. The length difference can now be compensated for by offsetting the fiber endfaces as depicted in Figure 1
, without an excessive amount of dispersion induced phase shifting.
Fig. 8. A cross section of the fringe pattern after the fibers were polished and aligned. The red trace is for the HeNe and the blue trace is for the 830nm laser diode. The zero order fringe is located pixel number 82.
After the polishing process was complete, the fibers were removed and each placed on a two-dimensional translation stage, which allowed the fiber separation and endface offset to be controlled. The fibers were aligned and the fringe pattern shown in Figure 8
These results indicate that the fibers are properly aligned such that the zero order fringe, aligned with pixel number 82, does not move when the source wavelength is switched between the 633 and 830nm source.
In this paper we have described our process for making a Young’s double pinhole interferometer. Since we are planning to determine the zero order fringe by using two different wavelengths, stringent requirements were placed on the phase difference of the light exiting the fibers. Using a white light interferometer, we are able to measure the length difference of the fibers during the polishing process. The final length difference measured was approximately 6µ
m. The shorter of the two fibers was then pulled back from the other to introduce a phase delay to obtain a final phase difference of less than 2π
/30. A plot of the two fringe patterns is provided (Figure 8
) which showed the alignment of the zero order fringes.
References and links
G. Indebetouw, “Profile measurement using projection of running fringes,” Appl. Opt. 17, 2930–2933 (1978). [CrossRef] [PubMed]
M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983). [CrossRef] [PubMed]
T. L. Pennington, H. Xiao, R. May, and A. Wang, “Miniaturized 3D surface profilometer using a fiber optic coupler,” submitted to Optics and Laser Technology, Jan 2000.
Optical Society of America, Handbook of Optics,W. G. Driscoll, ed. (McGraw-Hill, New York, 1978).
Z. G. Wang, Wavelength compensation in fused fiber couplers, Ph.D. Disseration, (Virginia Polytechnic Institute and State University, Blacksburg, VA, 1996).
T. Li, A. Wang, K. Murphy, and R. Claus, “White-Light Scanning Fiber Michelson Interferometer for Absolute Position-Distance Measurement,” Opt. Lett. 20, 785–787 (1995). [CrossRef] [PubMed]
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(150.6910) Machine vision : Three-dimensional sensing
Original Manuscript: April 7, 2000
Published: May 8, 2000
Timothy Pennington, Anbo Wang, Hai Xaio, and Russell May, "Manufacturing of a fiber optic Young's double pinhole interferometer for use as a 3-D profilometer," Opt. Express 6, 196-201 (2000)