1. INTRODUCTION

Space infrared telescope for cosmology and astrophysics (SPICA) [1], led by European and Japanese research groups, is a proposed next-generation space infrared observatory with a 2.5 m primary mirror cooled to below 8 K. The SPICA-far-infrared instrument (SAFARI) is one of three instruments of SPICA [2], which is an imaging Fourier transform spectrometer with a ${{2}}\;{\rm{ft}} \times {{2}}\;{\rm{ft}}$ (${\sim}{5.8} \times {{1}}{{{0}}^{- 4}} \times {5.8} \times {{1}}{{{0}}^{- 4}}$ in radians) instantaneous field of view for a wavelength of 34–230 µm. The designed sensitivity of the R–300 SAFARI/LR mode is about ${{5}} \times {{1}}{{{0}}^{- 20}}\;{\rm{W}}/{{\rm{m}}^2}$ (${{5}}\sigma$, 1 h) for a transition edge sensor detector with noise equivalent power (NEP) of ${{2}} \times {{1}}{{{0}}^{- 19}}\;{\rm{W}}/{\rm{H}}{{\rm{z}}^{1/2}}$. The calibration source assembly (CSA) is one of the components of SAFARI, which provides a uniform light source at 34–230 µm to calibrate the transition edge sensor readout circuit. To fulfill the requirements of the SAFARI calibration source, a terahertz (THz) integrating sphere is essential.

The function of the integrating sphere is to spatially integrate the input radiant flux, and to output a spatially uniform radiance. It can be regarded as a diffuser that preserves energy but removes spatial information of the incident power, equally distributing radiance regardless the view angle of the observer [3]. The reflection of the inner surface of the integrating sphere has to be diffusive or Lambertian-like. Therefore, the operating wavelength of the integrating sphere depends on their inner surface which can reflect the radiation diffusively.

For a short wavelength, coating with particular materials is the typical method to achieve the Lambertian-like surface. For example, magnesium oxide (MgO) [4–7], barium sulfate (BaSO4) [8], and polytetrafluoroethylene (PTFE) [7–9] are the common materials used in the surface coating of the integrating sphere for ultraviolet to visible light. The MgO layer has the absolute reflectance larger than 0.96 in the visible light. The PTFE exhibits high reflectance over 0.9 within 0.25–2.5 µm [near-infrared (NIR)] spectrum ranges. The gold-coated integrating spheres are also developed for the NIR spectrum [10]. For example, Labsphere Inc. developed diffuse gold integrating spheres with the reflectance over 0.90 within the wavelength range from 0.7 to 20 µm [8].

The reports on the integrating spheres operated at mid-infrared (MIR) and far-infrared (FIR) (THz) are very rare. Due to the long wavelength, material coating is not suitable for the surface preparation of an MIR/FIR integrating sphere. The group in SRON, the Netherlands Institute for Space Research, devoted to the development of an MIR and FIR integrating sphere for the CSA of SAFARI. The sandblasted and gold-coated metallic surface was used in their study. Several issues were addressed in their report [11]. The power is absorbed seriously by the crevasse structure on the sandblasted surface and the SiC sand would pollute the surface. Furthermore, the emissivity ($\varepsilon$) of the plated gold film is 0.08, which is higher than the expectation value and might lead to a higher power absorption. In addition, the gold film would smooth out the deep structure and reduce the surface roughness.

In this work, we report the development of an integrating sphere in the SAFARI wavelength with much improved performance. The sandblasting process, following the SRON group’s approach, was used to roughen the aluminum surface, and additionally an aluminum wet-etching process is introduced to “smoothen” the deep/sharp sub-structures. The surface topology studies confirmed the reduction of sub-structures. The surface reflectance of 0.91 was achieved. The output power measurement of the integrating sphere implies that the scattering of the surface is Lambertian-like.

 

Fig. 1. Surface topographic images of treated surfaces with the gold-plated layer. (a) The OM image of sandblasted surface without the aluminum wet-etching process. (b) The 3D profile of the square area in (a). Apparently, there are many sub-structures on the main structures after the sandblasting process. (c) The OM image of the sandblasted surface with the aluminum wet-etching process. (d) The 3D profile of the square area in (c). Most sub-structures are clearly removed after the aluminum wet-etching process.

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2. METHOD

The integrating sphere is made of aluminum with 5 mm wall thickness for preventing the distortion from machining and sandblasting. The sandblasting process was performed by a local machine shop using sapphire powder (size 1180–1400 µm) with pressure of ${{14}}\;{\rm{kg/c}}{{\rm{m}}^2}$. Most of the residual particles after the sandblasting process were removed by the ultrasonic bath cleaning, but few particles were still tightly embedded. The sandblasted aluminum surface was further etched by the commercial aluminum etching solution, Aluminum Etch 85-2-13 (Maxwave, Taiwan), which is a mixed solution of phosphoric acid (${{\rm{H}}_3}{{\rm{PO}}_4}$), nitric acid (${{\rm{HNO}}_3}$), acetic acid (HOAc), and water with the assay 76.7%, 1.2%, 8.5%, and 13.6%, respectively. The etching process was performed for two hours at the temperature of 60°C.

Due to the difficulties of measuring the curving surface inside the hemisphere of the integration sphere, we investigated the surface morphology of aluminum flat plates with the same surface treatment conditions instead. The surface profiles of the samples were measured by a confocal laser microscope, KEYENCE VK-X1000, and analyzed by the method of fast Fourier transform (FFT). The relative reflectance spectra of integrating spheres with 50 mm diameter and different inner surface conditions were measured by the Fourier transform spectrometer (FTS), FARIS-1 JASCO, with an external cryogenic bolometer (QGEB/0, QMC Instrument). The lamp temperature is 2900 K. The spatial uniformity of output power was studied by an x–z scanning stage (integrating a home-made halogen lamp source at a temperature of 2800 K, chopper, and 80 mm integrating sphere) and the QMC bolometer. To investigate radiation power at different frequencies, patterned metal-mesh bandpass filters with center wavelength at 70, 90, 200 µm (THORLABS) are used in front of the window of the cryogenic QMC bolometer.

3. RESULTS AND DISCUSSION

A. Surface Characterization

Figure 1(a) shows the optical microscope (OM) image of the sandblasted and gold-plated aluminum surface without the wet-etching process. Structures with a scale of few tens to few hundred micrometers were created by the sandblasted process, which fulfill the requirements for scattering the light with a wavelength range of 34–230 µm. However, the surfaces of these structures have many sub-structures. Figure 1(b) shows the three-dimensional (3D) optical microscope image of the area marked in Fig. 1(a). The maximum peak-valley height is up to 110 µm. Sub-structures such as sharp edge and complicated peaks are clearly observed. These sub-structures result in the high loss of surface even plated with a thick gold layer. The sub-structures were removed after the aluminum wet-etch process, as shown in Fig. 1(c). The 3D image, Fig. 1(d), demonstrates the smoothened surfaces. The maximum peak-valley height is reduced to 90 µm because the sharp structures are etched faster. Most sub-structures are clearly removed after the aluminum wet-etching process.

The line profiles of the surfaces with (blue line) and without (red line) the aluminum wet-etch process are shown in Fig. 2(a). The spatial resolution is 1.37 µm and the height of the profile of the without wet-etched sample was shifted intentionally. Being consistent with the OM images, the peak-valley height of the wet-etched surface has obviously reduced in comparing the one without the aluminum wet-etching process. To analyze the profile of the surface quantitatively, FFT analysis was used on each surface profile. The averaged amplitude of seven FFT spectra of surfaces with and without wet-etch are shown in Fig. 2(b). The FFT amplitude of the surface profile with the wet-etch process is reduced in all frequencies. The ratio of the average amplitude of the samples with (${{\rm{A}}_{{\rm{we}}}}$) and without (${{\rm{A}}_{{\rm{as}}}}$) the wet-etch process after being smoothed by FFT filtering is shown in the inset. The ${{\rm{A}}_{{\rm{we}}}}/{{\rm{A}}_{{\rm{as}}}}$ is less than 0.7 for all FFT wavelengths, particularly in the regime between 7 and 100 µm.

 

Fig. 2. Analysis of the as-sandblasted and wet-etched surface profiles. (a) The line profiles of samples measured by a confocal laser microscope. Apparently, the surface becomes smooth after the aluminum wet-etch process. (b) The averaged FFT spectra of the as-sandblasted and the wet-etched surface profiles. The FFT amplitude decreases significantly at the FFT frequency between 0.1 and 0.01 1/µm. Inset: the smoothed ratio [12] of FFT amplitudes (${{\rm{A}}_{{\rm{we}}}}/{{\rm{A}}_{{\rm{as}}}}$) of the surface profiles with and without aluminum wet-etching process reveals remarkable reduction between the FFT wavelength between 10 and 100 µm. (c) The PSD of the line profiles of unetched (red line) and etched (blue line) surfaces. The calculated 1D fractal dimension, ${{\rm{D}}_f}$, of the unetched surface is 1.2. The etched surface shows a ${{\rm{D}}_f}$ close to 1 and 1.5 at the low and high spatial frequency regions, respectively.

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Furthermore, the fractal dimension of the surface is also a good measure for evaluating the surface roughness. The one-dimensional fractal dimension ${{\rm{D}}_f}$ can be estimated by ${{\rm{D}}_{f}} = ({\rm{5 +}}\beta)/{{2}}$, where $\beta$ is the slope of the power spectrum density (PSD) versus spatial frequency of the line profile in log-log plot [13–15]. Figure 2(c) shows the PSD of line profiles of unetched and etched surfaces. The PSD of the unetched surface, red line, shows a linear dependence on the spatial frequency in the plot as the spatial frequency is larger than ${0.003}\;{{\unicode{x00B5}}}{{\rm{m}}^{- 1}}$. The calculated fractal dimension is about 1.2, indicating the surface has many sub-structures. After the wet-etching process, the calculated fractal dimension in the spatial frequency between 0.003 and ${0.04}\;{{\unicode{x00B5}}}{{\rm{m}}^{- 1}}$ is close to 1. The fractal dimension of close to 1 implies that the surface is “smooth” in the length scale larger than 25 µm (${{1/0.04}}\;{{\unicode{x00B5}}}{{\rm{m}}^{- 1}}$) after the wet-etching process. Interestingly, the fractal dimension increases to 1.5 in the high spatial frequency region, indicating that more fine structures in micrometer scale were created. More investigations are necessary to understand the reasons for the increase of fractal dimension in this region.

In short, the study on the surface profile demonstrated that the wet-etching process could substantially eliminate the sub-structures on the structured surface formed by the sandblasting process in the length scale larger than 25 µm. The trapping and absorption of the incident lights at 1–10 THz (30–300 µm in wavelength) due to the sub-structures could be significantly reduced.

B. Relative Reflectance Measurement

The surface reflectance is one of the key parameters for an integrating sphere. The input light becomes dimming in an integrating sphere with a low reflectance surface after many reflections. Ideally, the reflectance of a rough surface can be obtained by integrating the reflected power at different angles, ${P_r} = \int {{p_r}} (\theta ,\phi){\rm{d}}\theta {\rm{d}}\phi$, as shown in Fig. 3(a). In reality, the experimental setup for detecting the reflected power at all angles using a cryogenic detector in THz is not simple. The alternative method is to measure the output power of an integrating sphere. The incident light from the input port of the integrating sphere is scattered and reflected on the rough surface for many times. The output power of the integrating sphere is relatively easy to measure, but the angular information of reflected light will be lost, as shown in Fig. 3(b).

 

Fig. 3. Reflectance measurement methods. (a) The total reflected power ${P_r}$ is obtained by integrating the reflected power of the surface at different angles, ${p_r}(\theta ,\phi)$. The reflectance of the surface is calculated by ${P_r} /{P_i}$. ${P_{{\rm{abs}}}}$ is the absorbed power. (b) The reflectance of the surface can be calculated by incident power, ${P_i}$, and the measured output power of an integrating sphere, ${P_{{\rm{out}}}}$.

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According to the theory of the integrating sphere [16–19], the radiance of an illuminated sphere is

Thus, the reflectance of the integrating sphere under study can be obtained by calculating the output radiance ratio of the integrating sphere under study (${L_S}$) and the reference one (${L_R}$), $\gamma = {L_R}/{L_S}$, which yields the formula of

Three integrating spheres with different surfaces were prepared: smooth, sandblasted with and without the wet-etch process. The diameters of the integrating spheres are 50 mm and their inner surfaces are gold-plated. The sizes of input or output ports are 6 mm in diameter. The port factor $f$ is 0.0072, and Eqs. (2) and (3) are adequate for our analysis.

The schematically experimental setup for measuring the output power spectrum of an integrating sphere is shown in Fig. 4(a). The integrating sphere is mounted inside a FTS working in terahertz frequency with a halogen lamp light source. The output power of the integrating sphere was detected by a cryogenic bolometer (QMC Ltd). The output signal of the cryogenic bolometer was fed to the data acquisition system of the FTS system. Figure 4(b) shows the optics in the FTS sample chamber. A tubular light-guide (gold-plated surface) is used to confine the radiation angle at the output port, which improves the coupling of output power to the QMC detector.

 

Fig. 4. (a) Schematic drawing of experiment setup for measuring the surface reflectance of the integrating sphere. (b) The photo inside the FTS sample chamber. A conical horn is installed at the input port of the integrating sphere. To match the focal length of the coupling lens, a tubular lightguide is deployed at the output port. (c) The FTS spectra of the integrating sphere with different surfaces, smooth surface (blue lines in the upper and lower panels), sandblasted without wet-etch (red line in upper panel), and sandblasted with wet-etch (red line in the lower panel). The radiance of the integrating sphere with sandblasted and wet-etched surfaces is significantly enhanced.

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The output intensity spectra of the integrating sphere with different surfaces are shown in Fig. 4(c). The blue lines in the upper and lower panels of Fig. 4(c) are the output intensity spectra of the integrating sphere with smooth surface in the interested frequency region, which are used as the reference for the reflectance calculation. The red line in the upper panel of Fig. 4(c) is the output intensity spectra of the integrating sphere with a sandblasted but not wet-etched surface. Its intensity (${I_{\textit{sb}}}$) is much lower than that of the reference integrating sphere (${I_{\textit{sm}}}$), ${I_{\textit{sm}}}/{I_{\textit{sb}}}$ (or ${L_{\textit{sm}}}/{L_{\textit{sb}}}$) ${\sim}{{11}}$. This result implies that the power absorption of the sandblasted surface without the aluminum wet-etching process is significant, which is consistent with the early report from the SRON group [11]. By using Eq. (3), the estimated reflectance of the sandblasted and gold-plated surface is only 0.67 when the reflectance of the smooth gold-plated surface is 0.96 [20].

On the contrary, the integrating sphere after the sandblasting and wet-etching processes demonstrates intensity close to that of the one with the smooth surface [red line in the lower panel of Fig. 3(c)]. The ratio of ${I_{\textit{sm}}}/{I_{sb/we}}$ (or ${L_{\textit{sm}}}/{L_{sb/we}}$) is 1.4, indicating that the output power of the integrating sphere with the sandblasting and wet-etching processes surface remains nearly 70% of that with the smooth surface. The reflectance of the sandblasted/wet-etched/gold-plated aluminum surface is much improved to 0.91. Our observations indicate that the wet-etching process removes the complex sub-structures and makes the surface “smoother,” which improves the surface reflectance significantly.

C. Output Uniformity

As mentioned in the previous section, the angular information of reflected light on a surface is lost as an integrating sphere used to measure the surface reflectance. However, for an integrating sphere with ideal Lambertian surface, the radiation at the output port is close to a blackbody surface. Therefore, one can indirectly evaluate whether the surface reflection is Lambertian-like or not by measuring the spatial/angular power distribution at the output port.

 

Fig. 5. Measurement setup of output uniformity of the integrating sphere. The home-made light source, chopper, and integrating sphere were mounted on an x–z stage. The scanning range of measurement is 50 mm. A tunable aperture and bandpass filter are located in front of the window of the detector dewar.

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Fig. 6. Measured intensity profiles of the integrating sphere with an output port of 25 mm. The distance between the output port to the aperture is 14.5 mm. (a) The intensity profile without the bandpass filter (BPF). The aperture size is 2 mm. (b)–(d) The intensity profiles with the BPF of 70 µm, 90 µm, and 200 µm with the aperture size of 2 mm. The contours reveal circular and symmetrical profiles in the x and z directions for all cases, indicating the input light is well scattered in the integrating sphere.

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Figure 5 shows the measurement setup for evaluating the uniformity of radiation power at the output port. The integrating sphere for the measurement is 80 mm in diameter with an input port of 8 mm and an output port of 25 mm. The inner surface of the integrating sphere was sandblasted, wet-etched, and gold-plated as described in previous sections. The radiations from a home-made halogen lamp incident into the integrating sphere with a chopping frequency of 17 Hz. A baffle at the input port was installed to prevent from the incident light directly escaping to the output port without scattering. The integrating sphere, light source, and chopper are mounted on an x–z scanning stage. Radiation is detected by a cryogenic THz bolometer (QMC Ltd.) with a tunable aperture and a bandpass filter in front of the input window of the bolometer. Three bandpass filters with center wavelengths at 70, 90, and 200 µm were used to check the radiation power at different bands. The distance ($l$) between the output port of the integrating sphere and the detector system is 14.5 cm. The scanning range is 50 mm in both the x and z directions on the plane of the output port. The output signal of the bolometer was measured by a lock-in amplifier at the chopping frequency.

Figure 6 shows the measured intensity profiles of the integrating sphere (a) without and with (b) 70 µm (${\sim}{4.3}\;{\rm{THz}}$), (c) 90 µm (${\sim}{3.3}\;{\rm{THz}}$), and (d) 200 µm (1.5 THz) bandpass filters. The distance between the output port of the integrating sphere and the tunable aperture is 14.5 mm. The aperture size is 2 mm for measuring the signal without the bandpass filter but increased to 3 mm as the bandpass filter was installed. The contour of spatial mapping is circular and symmetrical in the $x$ and $z$ directions for all cases. The measured signal at a long wavelength becomes weaker, which is a natural property of radiance from a thermal source. These measured intensity profiles can be used to extract the spatial radiation profile at the output port of the integrating sphere by simulation.

The measured spatial distribution of the intensity in Fig. 6 is dependent on the spatial and angular radiation profile at the output port, the position and the size of the aperture, and the position and the coupling angle of the detector. The parameters of the last two are known, and the spatial and angular radiation profile at the output port is what we want to know. By assuming a certain spatial and angular radiation profile at the output port, one can calculate the intensity seen by the detector and compare the calculated result with the measured data. Then the most possible spatial and angular radiation profile at the output port can be determined.

The schematic configuration of the measurement setup for numerical calculation is shown in Fig. 7(a). The distance between the aperture and the coupling horn of the cryogenic bolometer is about 60 mm. The coupling angle of the horn, ${\theta _D}$, is about 5.5° and the aperture size of the horn is 10 mm. At a specific position of the integrating sphere to the aperture and detector, we summed up the contributions of all unit areas at the output port with blackbody radiation characteristics. Because of circular symmetry, the position of the integrating sphere for performing the calculation is only along the $x$ axis and the length is 50 mm to compare with experimental results.

 

Fig. 7. Simulation model. (a) The configuration of the experiment setup. The dimensions are the experimental parameters. (b) The comparison of simulation (red line) and experimental results. The intensity is normalized to the peak value. The simulated curve is based on the assumption of uniform radiance at the output port of the integrating sphere, and it is in good agreement with the experimental data.

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In the calculation, the size of the unit area at the output port is 0.025 mm, which is much smaller than the size of the output port of 25 mm. To further increase the accuracy, we set meshes with size of 0.3 mm at the aperture which is 2 mm and 3 mm in diameter in the measurement without and with the bandpass filter, respectively. The incident angle ${\theta _i}$ is determined by the position of the unit area at the output port and the position of the unit mesh at the aperture, as defined in Fig. 7(a). In our calculation model, the radiation from any unit area at the output port of the integrating sphere is seen by the detector only when two conditions are satisfied: (1) the incident angle ${\theta _i}$ is smaller than the coupling angle of the horn ${\theta _D}$, and (2) the projected position of the radiation, which is emitted from the unit area of the output port and passes through the aperture, is within the horn of the detector.

Figure 7(b) shows the normalized line profiles of experimental data and the simulation result with a radiance from blackbody-like surface at the output port. The consistency between simulation and experimental results indicates that blackbody-like radiance at the output port is a good model for our integrating sphere and implies the Lambertian-like scattering of the light inside the integrating sphere. It is noted that the profile with a 200 µm filter is relatively wider, which could be due to the diffraction fringe because the wavelength of light is close to the dimension of the aperture (3 mm).

4. CONCLUSION

A novel process, which combines sandblasting and aluminum wet-etching, was established to fabricate the rough surface with high reflectance at the THz region. With gold plated, the reflectance of the surface prepared by the novel process is around 0.91 as the reflectance of the flat gold surface is 0.96. This value is much higher than the reflectance of the surface prepared by the sandblasting process only, ${\sim}{0.67}$. The improvement is attributed to the reduction of complex sub-structures on the sandblasted surface by applying the aluminum wet-etching process. The FTS spectra show negligible wavelength dependence of reflectance in the region of 34–230 µm. The simulation result implies that the surface radiance of the output port is blackbody-like, indicating that the scattering of the light inside the integrating sphere could be Lambertian-like, which is similar to the conventional integration sphere.