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Foreign Direct Investment and Economic Growth: A Time Series Analysis of Turkey,
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1 Y.2013, Cilt 3, Sayı 2, ss Y.2013, Volume 3, Issue 2, pp Foreign Direct Investment and Economic Growth: A Time Series Analysis of Turkey, Eyup DOGAN Clemson University, the J.E. Walker Department of Economics, USA, Abstract This paper attempts to examine the causality relationship between foreign direct investment (FDI) and economic growth (GDPGR) in Turkey using the time-series techniques. All analyses are conducted with the annual data of foreign direct investment and real gross domestic product of Turkey over the period of The results of the ADF unit root test show that the time-series variable are nonstationary atlevels, but become stationary in the first differences. Besides, the results of the Johansen co-integration test indicate that both series are co-integrated and a positive long-run relationship exists between FDI and GDPGR. Findings of the Granger-causality method suggest that there is a bidirectional causalitybetween them. Keywords: Economic Growth, Foreign Direct Investment, the Johansen Co-integration test, the Granger Causality test JEL Classification Codes: F21, F43 Doğrudan Yabancı Yatırımlar ve Ekonomik Büyüme: Türkiye Üzerine Zaman Serisi Analizi, Özet Bu çalışmada Türkiye için doğrudan yabancı yatırımlarla (DYY) ekonomik büyüme arasındaki ilişki zaman serisi analizi kullanılarak incelenmektedir. Bu çalışmadaki tüm analizlerde, Türkiye için dönemini kapsayan doğrudan yabancı yatırımlar ve gayri safi yurtiçi hasılaya ait yıllık veriler kullanılmıştır. Zaman serisi verileri kullanılarak uygulanan ADF birim kök testi sonucuna göre değişkenlerin durağan olmadıkları fakat birinci fark değerlerinde durağan oldukları gözlenmiştir. Bununla birlikte, Johansen eşbütünleşme test sonucu iki serinin eşbütünleşik olduğunu ve DYY ile ekonomik büyüme arasında uzun dönemli pozitif bir ilişkinin devam ettiğini belirtmiştir. Granger nedensellik testi doğrudan yabancı yatırımlar ve ekonomik büyüme arasında iki yönlü nedensellik ilişkisinin olduğunu ortaya koymuştur. Anahtar Kelimeler: Ekonomik Büyüme, Doğrudan Yabancı Yatırımlar, Johansen Eşbütünleşme testi, Granger Nedensellik testi JEL Sınıflandırma Kodları: F21, F43 Atıfda bulunmak için Cite this paper Dogan, E. (2013). Foreign Direct Investment and Economic Growth: A Time Series Analysis of Turkey, Çankırı Karatekin Üniversitesi, 3(2),
2 1. Introduction Do countries need foreign direct investment inflow (FDI) in order to obtain feasible and relatively higher level of growth rates? Most undeveloped and developing countries have experienced insufficient amount of national savings to reach desirable growth rates. The Sunday Times (2001) reports that FDI must meet this investmentsaving gap. There are several channels how FDI promotes economies: UNCTAD (1999) reports that FDI helps economies to grow up through increases in the amount and efficiency of total investment in host countries; Wang (2009) argues that the target of FDI is stimulating the home countries GDPGR since capital movement and technological progress are the milestone of the economies; Bhattarai & Ghatak (2010) note that imports of the advanced technology management and marketing increase the efficiency in the levels of productions and distributions, the value of capital stock in the home countries, and the level of living standards and welfares in both host and foreign countries; Yılmazer (2010) indicates that FDI stimulates the GDPGR through increases in the usage of resources, the infrastructure investment, and the technological improvement. The undeveloped and developing countries including Turkey should thus take the advantage of FDI, while it intuitively looks for a country to go with respect to the potential profits and opportunities. Aitken & Harrison (1999) state that many countries simplify their regulations on FDI, and aggressively propose tax reductions and subsidies to get more of available FDI into their own lands. Ford et al. (2008) indicate that several governments assign their public departments to pull more FDI towards their own homelands using the reserved amount of public funds. This implies that the countries are willing to bear some costs to do so. In conjunction with the theoretical arguments from the existing literature, statistics about Turkey show that the amount of FDI increased from $0.075 billion in 1979 to $16 billion in 2011 and the value of GDP increased from $69 billion in 1979 to $775 billion in This remarkable and simultaneous increase in both variables takes my attention. The purpose of this study is investigating the relationship between foreign direct investment inflows and economic growth inturkey in the period of 1979 and 2011 applying time-series techniques, namely the Augmented Dickey-Fuller unit root test, the Johansen co-integration test, and vector error correction model (VECM). I also test the direction of linkage between FDI and GDPGR by the Granger causality test. This study differs from the old papers as it works with the most updated data, and examines the pure connection between GDPGR and FDI in Turkey. I organize the shape of this paper as follows: the second section brings literature review up, the third section provides further information about the data and 240
3 E.Dogan Güz/Fall 2013 Cilt 3, Sayı 2, ss Volume 3, Issue 2, pp methodology, the forth section exhibits the estimation process and results, and the last section summarizes the paper. 2. Literature Review A fair amount of theoretical and empirical papers find a positive relationship between foreign direct investment and economic growth, while a few support the opposite side. For example of opposite views, Blomstrom et al. (1992) divide 78 developing countries into two groups as low-income and high-income countries, and exert that there is no tie between FDI and GDPGR in the low-income countries although there is a positive effect of FDI on GDPGR in the high-income countries. Carkovic & Levine (2002) do not find a significant effect of FDI on economic growth if the host and foreign countries are at different levels of trade-openness. Umeora (2013) does not find FDI to have any effect on GDPGR in a case study of Nigeria over the period One of the earlier works by Wallis (1968), on the other hand, reports that an increase in FDI from the U.S.A. to the European Union promotes the economic growth in the receiving region. Mello (1999) uses the panel data model, and finds a positive relationship between the variables in the long run. Bosworth & Collins (1999) examine 85 countries (62 developing and 23 developed countries) for the years of , and expose a positive relationship between FDI and GDPGR. Xu (2000) studies the effect of FDI on GDPGR for 40 undeveloped and developing countries to where FDI flows from United States, and concludes that FDIpositively impact the growth if the minimum amount of human capital exists. Ericson & Irandoust (2001) applythe Granger causality test on several countries over the period 1970 through1997, state a unidirectional causality from FDI to growth in most countries. Basu et al. (2003) use a co-integration test on 23 developing countries between 1978 and 1996, and expose a long-run linkage between them. Bhattarai & Ghatak (2010) estimate a model using the panel data for 30 OECD countries for the years , and argue that FDI inflow positively affects GDPGR. Antwi et al. (2013) find that FDI contributed to economic growth in Ghana over the period 1980 through The studies that work on a case study of Turkey show various results. Such as Aslanoglu (2002) finds there is no straightforward causality relationship between FDI and GDPGR applying the Granger causality test in the period of 1975 and Alici & Ucal (2003) perform vector autoregression (VAR) model and the Toda Yamamato causality test and reveal that no significant connection between FDI and GDPGR exists. Alagoz et al. (2008) do not find a linkage between the variables employing the Granger causality test over the period 1992 through Kahramanoglu (2009) 241
4 investigates the relationship of FDI and GDPGR in two separated periods of and , and concludes that a bi-directional causality occurs between FDI and GDPGR along the second period, whereas there is a one-way causality running from GDPGR to FDI in the first period. Yılmaz et al. (2011) apply a timeseries methods on the presence of linkage between FDI and GDPGR for Turkey in the period of , and find that both series are co-integrated and have a longrun relationship. Ekinci (2011) reveals that there is a two-way causality between GDPGR and FDI applying time-series techniques over the period 1980 through Data and Methodology The data used in this study arethe aggregate annual time series at constant prices for real gross domestic product (GDP) and total net inflows of foreign direct investment (FDI) covering the period of in 33 pairs of observations. GDP is commonly used to represent economic growth. The data are drawn from the World Bank s World Development Indicators and in U.S. billion-dollars. Aggregates are based on 2000 U.S. dollars, and converted from domestic currencies using single year official exchange rates by the World Bank. The data are available in Appendix A. The relationship between foreign direct investment inflow and economic growth in Turkey is stated as: and, FDI t = π 0 +π 1 GDPGR t + ζ t GDPGR t = Ϯ 0 +Ϯ 1 FDI t +η t where the parameters ζ and η are normally distributed error terms. 4. Estimations and Results 4.1. Unit Root Test The purpose of applying the unit root test is empirically examining whether a timeseries contains a unit root. If the series has a unit root, it is said to be non-stationary; otherwise, the series is considered as stationary. A stationary variable is observed when the mean, variance, and auto-covariance of the time-series are constant along time according to Enders (2004). When the variables are non-stationary, Granger & Newbold (1974) state that one is likely to get a spurious regression which has a high R 2 (goodness of fit) and statistically significant coefficients although these series are actually unrelated, and implies that the results are without any economic meaning. 242
5 E.Dogan Güz/Fall 2013 Cilt 3, Sayı 2, ss Volume 3, Issue 2, pp Figure 1: Trends of LFDI and LGDP of Turkey ( ) After a brief look at the figure 1, one can notice non-zero mean and trend over time. This signs that both variables contain a unit root; however, I must apply a statistical test to prove it is the actual case. One of the most popular methods is the Augmented Dickey-Fuller (ADF) unit root test (Dickey & Fuller, 1979) to finalize whether the series are stationary or not. The ADF unit root test takes the following form (1): k X t =α + βx t-1 + i Xt i + γt + ε t (1) i 1 The ADF test concludes whether there is a unit root in X t, namely FDI and GDP. In the regression, ε t is a normally distributed white noise error term, T represents for a deterministic time trend, X t-1 are the lagged values of the mentioned variables, γ,λ,β,α are the estimated parameters, and X t-i is the lagged values of the first differences. Instead of applying Autoregressive (AR) analysis, the right lag length is determined by the method of Said and Dickey (1984), k = N 1/3, where N is the number of observations and k is the optimal lag length. An important step is selecting the right lag length (k) for the test process because of two reasons: (1) if k is too small some serial correlation can be left in the errors and the test can be biased, (2) if k is too large the power of the test willbe lower.this method suggests that the appropriate lag length is 3 in the ADF process as the data have 33 pairs of observations. Logarithmic values of the observations in the time-seriesdata are first used in order to assess a stationary series, where LFDI and LGDP represent for log of FDI and log of GDP, respectively. The null hypotheses in table 1 are that LFDI has a unit root in the 243
6 first case and LGDP has a unit root in the second case, and the alternative hypotheses are that neither of them has a unit root. The result of ADF process in the table 1 includes an option of trend and constant because the Figure 1 suggests that the variables have them. Both the z-scores and p-values yield that LFDI and LGDP havea unit root, because I fail to reject the null hypothesis at 5% level of significance as it falls within the acceptance interval. Hence, both variables are said to be nonstationary. Table 1: The Result of ADF Unit Root Test at Levels 1% Critical Value 5% Critical Value 10% Critical Value Variable z(t) Test Statistic p-value for z(t) Decision LFDI Fail to Reject LGDP Fail to Reject One of best ways is taking the first differences of the time-series to attaina stationary series if the time-series are concluded to be non-stationary. Thus, I take the first differences of LFDI and LGDP. Figure 2: First Differences of LFDI and LGDP of Turkey ( ) After a quick glance at the figure 2, the pairs of observations seem to exhibit meanreverting behavior, and have constant variances over time. This implies that the 244
7 E.Dogan Güz/Fall 2013 Cilt 3, Sayı 2, ss Volume 3, Issue 2, pp variables are likely to have no unit root; however, I must again follow ADF unit root test to make it statistically meaningful. The null hypotheses and the alternative hypotheses in the table 2 are set in the same way just as in the previous process, but ADF process is run without an option of constant and trend in this step. Because the test statistic is smaller than the critical value, and does not fall within the acceptance interval at 5% level of significance, the null hypotheses of havinga unit root are rejected for both series. Therefore, the variables now become stationary and are integrated in order one, I (1). Table 2: The result of the ADF Unit Root Test on the First-Differences 1% Critical Value 5% Critical Value 10% Critical Value Variable z(t) Test Statistic p-value for z(t) DLFDI Reject DLGDP Reject Decision Tari (2005) explains that two or more time-series data could be co-integrated if they are integrated in the same order, and these variables atlevels do not cause a spurious regression. Thus, co-integration techniques are applied onto LFDI and LGDP as both of the time-series are I(1) Co-integration Test Co-integration explains that one or more linear combinations of time-series variables are stationary even though they are individually non-stationary according to Dickey et al. (1991). In other words, if two or more series are individually integrated in the same order but some linear combination of them have lower order of integration, then the series are said to be co-integrated. Granger & Newbold (1974) report that a possible presence of co-integration has to be taken into account when one select a method to make a hypothesis on the relationship between two non-stationary variables. Before moving to co-integration test, I firstly need to determine the optimal laglength using the criteria such as AIC, BIC, and SIC. I then employ the following output in the table 3 to pin down the optimal lag-length. Indeed, the stars show that the lag-length is one. Please note that information criteria have to be minimized, and that's the reason why the stars are shown at certain values. 245
8 Table 3: Lag Length Selection Criteria Lag LL LR df p FPE AIC HQC SBIC * * * * * After selecting the right length, the Johansen ML co-integration test by Johansen (1988, 1991) is used to determine whether LFDI and LGDP are co-integrated.the Johansen multivariate co-integration test involves the proof of relationship between the time-series, takes the following vector auto-regression (VAR) model equation (2): ΔlnY t = + Π lnyt-i + ε t (2) where Y t represents n*1 vector of I (1) variables, namely foreign direct investment(fdi) and gross domestic product(gdp). Parameter and Π represent for n*n matrix of coefficients to be tested. All I need to know is that if the rank is zero, there will be no co-integrating relationship. If the rank (r) is one there will be one cointegrating relation, if it is two there will be two co-integrating relations and so on. When there is a co-integration between two time-series, these series have a long-run relation and cannot move too far away from each other. This test is based on maximum likelihood estimation and two statistics: maximum eigenvalue (K max ) and a trace-statistics (λ trace), where the λ trace statistic tests the null hypothesis that r is equal to zero (no co-integration) against a general alternative hypothesis of r>0 (co-integration). The K max statistic tests the null hypothesis that the number of co-integrating vectors is r co-integrating vectors versus the alternative of r+1 co-integrating vectors. The result in the table 4 indicates that the null hypothesis of no co-integration is rejected for rank of zero at 5% level of significance since trace statistic is bigger than 5% critical value. In the next step, the null hypothesis of 1 cointegrating equation versus 2 co-integrating equations cannot be rejected at 5% level of significance as trace statistic is smaller than 5% critical value. I finally conclude that there is one co-integrating equation that allows us to identify vector error correction mechanism, is covered in the next part. 246
9 E.Dogan Güz/Fall 2013 Cilt 3, Sayı 2, ss Volume 3, Issue 2, pp Table 4: The result of the Johansen ML Co-integration test Maximum Rank parms LL eigenvalue trace statistic 5% critical value * Vector Error Correction Mechanism If two time series are co-integrated by a common factor (co-integrating vector) it is not possible to use a standard Vector Autoregression (VAR) Model. I have to account for this relationship and use a Vector Error Correction Mechanism (VECM) which adjusts both short run changes in variables and deviations from equilibrium. I also have to make sure that the estimated parameter of equation one in VECM will be negative and statistically significant if VECM is a correct technique to go with. The negative sign guarantees that deviations in the short-run make the long-run equilibrium exist over time. The table 5 shows that the coefficient of equation one is and statistically significant at 5% level. Besides, error correction mechanism works and any shortterm fluctuations between the time series of GDPGR and FDI lead to a stable positive long run relationship since the value of coefficient lies down between zero and minus one. Referring to the definition by Ghatak (1998), nearly 46% of disequilibrium is corrected each year. Table 5: The Result of Vector Error Correction Model Co-integrating equations Equation Parms chi2 P>chi2 _ce Identification : beta is exactly identified Johansen normalization restriction imposed _ce1 beta Coef. Std. Err. z P> z [95%Conf. Interval] lgdp lfdi _cons
10 Granger (1988) argues that if two series are co-integrated, there must be a Grangercausality in at least one direction. I accordingly examine the Granger causality test in the next section to investigate the direction of linkage between LFDI and LGDP Granger Causality Granger (1988) reports that the Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another. It can be relevant only when the variables are either stationary or non-stationary but cointegrated, can be written as: lngdp t = α 1 + β 1 lngdp t-1 +β 2 lngdp t-2 + +δ 1 lnfdi t-1 + δ 1 lnfdi t ε 1t (3) lnfdi t = α 2 + +γ 1 lnfdi t-1 + γ 2 lnfdi t-2 + λ 1 lngdp t-1 +λ 2 lngdp t ε 2t (4) where ε 1t and ε 2t are white noise error terms, and β, δ, γ,λ are the parameters which tell how much the past values of the variables can explain the current value of either series. The null hypothesis in general is variable X does not Granger cause variable Y. In our example there are two null hypotheses: Foreign direct investment does not Granger cause economic growth (GDPGR), and economic growth does not Granger cause FDI. The null hypothesis of no Granger causality cannot be rejected if and only if no lagged value of an explanatory variable is retained in the regression (3) and or in the regression (4). Table 6: The Result of the Granger Causality Test Equation Excluded chi2 df Prob>chi2 LGDP LFDI LGDP ALL LFDI LGDP LFDI ALL The result in the table 6 indicates that I reject the null hypotheses. Hence, GDPGR Granger Causes FDI just as FDI Granger Causes GDPGR at 5% significance level, meaning that there is a two-way (mutual) causality effect between foreign direct investment and economic growth. 5. Summary and Conclusions This study attempts to investigate the relationship between foreign direct investment (FDI) and economic growth (GDPGR) using the annual data over the period of
11 E.Dogan Güz/Fall 2013 Cilt 3, Sayı 2, ss Volume 3, Issue 2, pp The processes of this paper show that a positive long-run relationship exists between the variables. The ADF unit root test suggests that the variables are nonstationary at levels, but become stationary in the first differences. The Johansen cointegration test indicates that there is long-run relationship between FDI and GDPGR, and the effect is significant. Also, finding of Granger causality states that there is a bi-directional causality between FDI and GDPGR. As Kahramanoglu (2009) suggests, the results of this study imply that a positive change in the level of production of goods and services is likely to increase the FDI in Turkey. Besides, politics and economists in Turkey should give more attention on attracting higher levels of foreign direct investment into Turkey in order to promote economic growth. Appendix A: Year GDP FDI Year GDP FDI Year GDP FDI Source: World Bank (http://data.worldbank.org ) References Alagoz, M., Erdogan, S., & Topalli, N. (2008). Doğrudan Yabancı Sermaye Yatırımları ve Ekonomik Büyüme: Türkiye Deneyimi Journal of Social Science at Gaziantep University, 7(1), Aitken, B., & Harrison, A. (1999). Do Domestic Firms Benefit from Foreign Direct Investment? Evidence from Venezuela. American Economic Review, 3, Alıcı, A.A., & Ucal, M.Ş. (2003). Foreign Direct Investment, Export and Output Growth of Turkey: Causality Analysis. Paperto be presented at the European Trade Study Group (ETSG) Fifth Annual Conference, Universidad Carlos III de Madrid,
12 Antwi, S., Mills, E., Mills, G., & Zhao X. (2013). Impact of Foreign Direct Investment on Economic Growth: Empirical Evidence from Ghana. International Journal of Academic Research in Accounting, Finance and Management Sciences, 3(1), Aslanoglu, E. (2002). The Structure and the Impact of Foreign Direct Investment in Turkey. Journal of Faculty of Economics at Marmara University, 17(1), Basu, P., Chakraborty, C., & Reagle, D. (2003). Liberalization, FDI and Growth in Developing Countries: A Panel Co-integration Approach, Economic Inquiry, 41(3), Bhattarai K., & Ghatak, S. (2010). FDI, Investment and Growth in OECD Countries.Economics Discussion Paper, 2010/5, Kingston. Blomstrom, M., Robert, E.L., & Mario, Z. (1992). What Explains Developing Country Growth. NBER Working Paper Bosworth, B., & Collins, S.M. (1999). Capital Inflows, Investment and Growth. Tokyo Club Papers,12, Carkovic, M., & Ross, L. (2002). Does Foreign Direct Investment Accelerate Growth. MIMEO, University of Minnesota. Dickey, D.A., & Fuller, W.A. (1979). Distributions of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74, Dickey, D.A., Jansen, D.W., & Thornton, D.L. (1991). A Primer on Co-integration with an Application to Money and Income. Journal of Federal Reserve Bank of St. Louis, Ekinci, A. (2011). The Effect of Foreign Direct Investment on the Employment and Economic Growth: the Case of Turkey ( ). Journal of Economics and Administrative Sciences, Eskişehir Osmangazi University, 6(2), Enders W. (2004). Applied Econometric Time Series. Second Edition, New Jersey: John Wiley & Sons, Inc. Ericsson, J., & Irandoust, M. (2001). On the Causality between Foreign Direct Investment and Output: A Comparative Study. The International Trade Journal, 15(1),
13 E.Dogan Güz/Fall 2013 Cilt 3, Sayı 2, ss Volume 3, Issue 2, pp Feldstein M., & Horioka, C. (1980). Domestic Saving and International Capital Flows. Economic Journal, 90(358), Feldstein M. (1995). The Effects of Outbound Foreign Direct Investment on the Domestic Capital Stock. NBER Working Paper No Ford, T., Rork, J., & Elmslie, B. (2008). Foreign Direct Investment, Economic Growth, and the Human Capital Threshold: Evidence from US States. Review of International Economics, 16(1), Ghatak, A. (1998). Aggregate Consumption Function for India: A Co-integration Analysis under Structural Changes Journal of Applied Statistics, 25(4), Granger, C.W.J. (1988). Some Recent developments in a Concepts of Causality. Journal of Econometrics, 39(1-2), Granger, C.W.J., & Newbold, P. (1974). Spurious Regressions in Econometrics. Journal of Econometrics, 2, Guidotti, P.E., & De Gregorio, J. (1992). Financial Development and Economic Growth. IMF Working Papers 92/101, International Monetary Fund. Johansen, S. (1988). Statistical Analysis of Co-integration Vectors. Journal of Economic Dynamics and Control, 12(2-3), Johansen, S. (1991). Estimation and Hypothesis testing of Co-integration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), Kahramanoglu, İ.E. (2009). Uluslararası Doğrudan Yatırımların Ekonomik Büyümeye Etkisi ve Ülkelerin Hazmetme Kapasitesi Türkiye Örneği. Expert Thesis of Undersecretaries of Treasury, Mello, L.R. (1999). Foreign Direct Investment-Led Growth: Evidence from Time Series and Panel Data. Oxford Economic Papers, New Series, 51(1), Said, E., & Dickey, D.A. (1984). Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order. Biometrika, 71, Sen, A., & Saray, M.O. (2010). Türkiye de Doğrudan Yabancı Sermaye Yatırımlarının Ekonomik Büyümeye Etkisi: Panel Veri Analizi. Journal of Academic Resources and Studies,
14 Tarı, R. (2005). Ekonometri. 3th Edition, Istanbul: Publications of Kocaeli University, No: 172. Umeora, C.E. (2013). Effects of Foreign Direct Investment (FDI) on Economic Growth in Nigeria. SSRN Working Papers (June 26, 2013) UNCTAD. (1999). World Investment Report United Nations, New York and Geneva. Wallis, K.F. (1968). The E.E.C. and United States Foreign Investment: Some Empirical Evidence Re-Examined. The Economic Journal, 78(311), Wang, M. (2009). Manufacturing FDI and Economic Growth: Evidence from Asian Economies. Applied Economics, 41, Xu, B. (2000). Multinational Enterprises, Technology Diffusion and Host Country Productivity Growth. Journal of Development Economics, 62, Yilmaz, O., Kaya, V., & Akinci, M., (2011). The Effect of Foreign Direct Investment on Economic Growth in Turkey ( ). Journal of Faculty of Economics, Atatürk University, 25(3-4), Yılmazer, M. (2010). Doğrudan Yabancı Yatırımlar, Dış Ticaret ve Ekonomik Büyüme İlişkisi: Türkiye Üzerine Bir Deneme. Journal of Social Science, Celal Bayar University, 8(1),
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text:
|Publication number
|Publication type
|Application number
|Publication date
|Jun 21, 1983
|Filing date
|Mar 23, 1981
|Priority date
|Mar 23, 1981
|Fee status
|Publication number
|David W. Jackson
|Original Assignee
|Probe Systems, Inc.
|Export Citation
|BiBTeX, EndNote, RefMan
|Patent Citations (4), Referenced by (32), Classifications (5), Legal Events (8)
|External Links: USPTO, USPTO Assignment, Espacenet
This invention relates to the field of signal processing, and in particular, to optical signal processing utilizing coherent detection.
Signal processing typically involves the modulation of a source signal by an information signal to produce a modulated signal. The modulated signal, after transmission and any appropriate processing, is demodulated to recover the information signal, as modified by the processing.
Coherent detection, sometimes called synchronous detection, is a method of detection in which the demodulation employs a reference signal, sometimes called a local oscillator signal, that is in synchronisim with the source signal.
In optical processors, the input information signals are typically time-varying electrical signals which modulate optical source signals to produce optical, modulated signal. The optical, modulated signals are processed and then demodulated to produce electrical output information signals. The modulation converts the electrical signals to optical signals and the demodulation converts the optical signals back to electrical signals. The conversion from electrical to optical signals is undertaken because the desired signal processing can be performed better optically than it can be electrically.
In laboratory environments, coherent-detection optical processors have been known in the prior art. In such processors, coherent light from a laser source is diverted into two paths by means of beam-splitters and mirrors. One path passes the optical source beam through a modulator to modulate the source beam with an appropriate input information signal. The other path from the laser source is transmitted withot modulation to form a coherent reference signal. The reference signal is added to the modulated signal to enable coherent detection. Because the reference signal and the modulated signal travel in different paths, careful alignment of the beam-splitters, mirrors, and other optical elements is required in order to achieve satisfactory coherent detection. Relative displacement between the modulated signal and the reference signal by one-half of a wavelength (for example, less than a micron) can cause complete phase reversals which change the phase of the output information signal by 180 degrees. Because ot the careful alignment and high stability required in prior art coherent-detection optical processors, they have been generally regarded as impractical except in laboratory environments.
Optical processors for real-life cross-correlation have recognized the extreme alignment sensitivity of the modulated signal and the reference signal beams. Vibration of the apparatus or inhomogeneities of the optical mediums usually cause optical path differences which substantially interfere with the desired processing. In order to overcome such problems, collinear heterodyning has been proposed.
Collinear hetrodyning is described, for example, in the article "Collinear Heterodyning and Optical Processors" by Herbert R. Carlton, William T. Maloney and Gerald Meltz, Proceedings of the IEEE, Vol. 57, #5, May 1969, pages 769-775. In that article, a real-time cross-correlator is described in which the reference signal and the modulated signal are collinear and hence are not subject to error-causing optical path differences and other problems created by the use of separate optical paths.
Other optical processors have been known which employ collinear optical processing. Such systems, however, have not provided a satisfactory method of and apparatus for processing wide-bandwidth information signals to provide wide-bandwidth output signals.
In light of the above background, there is a need for a wide-bandwidth, high-resolution stable optical processor employing coherent detection.
The present invention is a method of and an apparatus for coherently detecting modulated optical signals employing optical mask-generated signals.
A coherent light source generates a source beam which is incident on a spatial light modulator. The spatial light modulator modulates the source beam with an information signal. The information signal, typically a wide-band radio frequency signal, is composed of one or more frequency components within its frequency bandwidth. The modulated beam output from the spatial light modulator includes corresponding frequency components resulting from the modulation. The frequency components output from the modulator diverge and become spatially separated. One of the frequency components of the modulated beam is the zero frequency component (DC component) which corresponds to the unmodulated source beam.
A reference beam is formed from the zero frequency component by a reference beam generator. The reference beam is generated so as to appear to diverge from a reference point located at or near the spatial light modulator.
An optical detector is located to receive the reference beam and particular ones of the spatially separated frequency components corresponding to the frequency components of the input signal.
The optical detector performs coherent detection by squaring the sum of the frequency components and the reference beam to provide an output information signal as a function of the input information signal.
In accordance with a preferred embodiment, the reference beam generator is formed by a Fourier transform lens and an optical mask.
The Fourier transform lens transforms the modulated beam to spatially separate the frequency components. At the transform lens focal plane, the zero frequency component appears at one point and the other frequency components appear at different points displaced from the zero frequency point. The optical detector aperture is offset from the zero frequency point to receive only those frequency components which correspond to the frequency components of the input information signal. The detector is typically located at or near the transform lens focal plane.
In order to enable coherent detection, an optical mask is provided for diffracting the zero frequency component to provide a coherent reference beam across the full detector aperture. The resultant signal at the detector aperture is the sum of the coherent reference beam, produced by the optical mask, and the spatially distributed frequency components falling within the aperture. In general, the optical mask is located anywhere between the light source and a position in front of the detector; and hence, the optical mask can be placed on either side of the spatial light modulator or on either side of the Fourier transform lens.
The optical mask utilized to produce the coherent reference signal is produced by holographic, digital or any other suitable technique. In a holographic method, a coherent light beam is split by a beam splitter into two spatially separate paths. The beam in one path is analogous to the modulated beam previously described but it is unmodulated as it passes through the Fourier transform lens. The beam in the other path is focused and recombined with the unmodulated beam to expose a photographic or other plate located at the position that the optical mask is to be placed. Exposure and development of the plate produces the desired optical mask.
In accordance with a preferred embodiment of the present invention, the optical mask is located between a Fourier transform lens and the detector aperture at a position which optimizes the coherent reference beam signal strength. The location of the mask is determined by the geometrical relationship between the zero frequency component and the optical elements. The zero frequency component forms a cone of light from the Fourier transform lens converging at a point at the Fourier transform focal plane. A portion of the converging zero frequency component is diffracted by the optical mask to form the reference beam. The reference beam is a diverging cone which fills the detector aperture such that a virtual image point appears to be a point located in a plane passing through the spatial light modulator. For maximum efficiency, the optical mask is located approximately at a point such that the ratio of the width of the diverging reference cone as it passes through the optical mask and the width of the converging zero frequency cone at the position of the optical mask is a maximum.
With the coherent reference beam provided in the manner summarized above, the objective of providing stable coherent detection for wide-bandwidth optical processors of many types is achieved.
Additional objects and features of the present invention will appear from the following description in which the preferred embodiments of the invention have been set forth in detail in conjunction with the drawings.
FIG. 1 is a block diagram depicting an optical processor, employing coherent detection in accordance with the present invention positioned to receive an input information signal S(t) and to produce an output information signal I(t).
FIG. 2 is a block diagram of an optical processor in accordance with one embodiment of the present invention.
FIG. 3 is a more detailed schematic diagram of the optical processor of FIG. 2.
FIG. 4 is a schematic optical diagram further depicting optical ray traces between optical elements of the FIG. 3 device.
FIG. 5 is a schematic representation of the optical configuration employed for holographically generating an optical mask for use in the apparatus of the present invention.
In FIG. 1, the signal source 10 provides an input information signal S(t) on line 13 to the optical processor 11. The signal S(t) is typically a radio frequency signal with wide bandwidth. A typical signal has a 200 MHz center frequency with a 100 MHz bandwidth.
Optical processor 11 receives the S(t) signal and optically processes that signal. The optical processing in one example delays the signal S(t). Other types of processing include frequency filtering, excising (removing unwanted frequency components), matched filtering, correlation, and phaseshifting. In order to perform such other types of processing, optical elements, in addition to those shown in FIGS. 2, 3 and 4, are generally required. For example, a frequency plane modulator can be added when frequency filtering or excising is desired.
After optical processing, the processor 11 forms the output information signal I(t) on line 14 where I(t) is a function of the input information signal S(t). The output device 12 receives the signal I(t) for further processing and/or use.
The FIG. 1 apparatus is employed in many applications. In a typical application, the signal S(t) is a frequency down-shifted radar signal in a radar receiver where wide-bandwidth processing of the signal S(t) is required. For example, unwanted frequency components can be removed from the signal S(t) and/or the signal S(t) may be suitably delayed.
In FIG. 2, the optical processor 11 of FIG. 1 is shown in further detail. Coherent light source (CLS) 15 is any source which produces spatially coherent light. Typically, source 15 is a conventional gas or solid-state laser together with appropriate lenses. A suitable gas (HeNe) laser commercially available has a center frequency of 4.741 times 1014 Hz and produces approximately five milliwatts of output power. Alternatively, a conventional source directed through a pinhole filter can be employed for source 15. While the source can have relatively high temporal coherence (for example, a fractional bandwidth of 10-6), sources with relatively low temporal coherence (for example, fractional bandwidths of 10-3 or greater) are acceptable.
The spatial light modulator (SLM) 16 receives the coherent source beam 22 from the coherent light source 15 and modulates the source beam with the input information signal S(t). The spatial light modulator 16 is typically a Bragg cell or other acousto-optical modulator. The modulated beam 23 is received by the Fourier transform lens (FTL) 17 which functions to transform beam 23 into beam 24 which has spatially separate frequency components at the back focal plane 33 of lens 17. The beam 24 includes frequency components corresponding to the frequency components in the input information signal S(t) and also includes the zero frequency or unmodulated frequency component derived directly from the source beam 22. The optical mask 18 operates on the unmodulated zero frequency component of the beam 24 to provide a coherent reference component to the beam 25. The beam 25 is incident, through the aperture 20, on the photodetector (PD) 19. The photodetector 19 coherently detects the modulated beam employing the coherent reference beam added by the optical mask 18.
The photodetector (PD) 19 is a conventional detector. Vacuum tube multipliers, avalanche photodiodes, PIN photodiodes and other conventional wide-band photodetectors are suitable large-bandwidth devices. The bandwidth of commercially available detectors can be as much as 2 gigahertz. Such detectors are squaring devices which respond to the incident optical power appearing at the aperture 20. In the present invention, the detector squares the vector sum of the incident optical signals, specifically, the incident modulated beam and the incident reference beam. The output signal I(t) on line 14 is a time-varying electrical signal having a readily isolatable frequency component proportional to the input signal S(t). Typically, the signal on line 14 is passband or high-pass filtered to isolate the component proportional to the signal S(t) from other unwanted components. Such filtering devices are conventional and can form a part of output device 12 of FIG. 1.
In FIG. 3, further details of the optical processor in accordance with the present invention are shown. In FIG. 3, the coherent light source (CLS) 15 includes a conventional highly coherent laser 27, a cylindrical lens 28 for diverging the light 28 to an appropriate size for the aperture of the spatial light modulator 16. The lens 29 receives the beam from lens 28 and forms the collimated source beam 22. Of course, other methods of generating a collimated source beam can be employed. The source beam 22 is incident on the spatial light modulator 16 in a direction substantially parallel to the X axis and normal to the Y axis where the Y axis is normal in the positive direction into the plane of the drawing.
The spatial light modulator 16 receives the input information signal S(t) on line 13 which causes acoustical waves to be propagated through the modulator in the direction of the negative Z axis. The acoustical waves transmitted through the modulator 16 create, as a function of time and position, points of varying index of refraction. The source beam 22 is diffracted differently, therefore, as a function of time and of spatial position along the Z axis. The acoustical wave is propagated as a function of the frequency components in the input information signal S(t). Therefore, the output beam 23 includes optical frequency components directly resulting, by the modulation process, from the electrical frequency components in the input information signal S(t). In order to enhance the diffraction of beam 22, the spatial light modulator 16 is normally rotated in a counter-clockwise direction by a small angle, φi (not shown in FIG. 3).
The Fourier transform lens (FTL) 17 forms at the back focal plane 33 the Fourier transformed image of the beam 23. The transformed image includes the image from the zero frequency component cone 30 (delimited by single-headed rays) which is incident at a central point of the back focal plane 33. Additionally, the beam 24 includes one or more frequency components each converging to a different point within aperture 20. The converging cone 31 (delimited by the triple-headed rays) is shown as typical and represents a single component frequency. The cone 31 is representative of one frequency within the bandwidth of the signal S(t). Each different frequency within the bandwidth of the signal S(t) will produce a different cone, like cone 31, incident at a different position in the direction of the Z axis and in the aperture 20 in FIG. 3.
In FIG. 3, the optical mask (OM) 18 is positioned at some displacement x from lens 17 and some displacement g from the modulator 16 as measured along the X axis. The mask 18 is positioned to receive at least a portion of the zero frequency component represented by cone 30 (delimited by the single-headed rays). Optical mask 18 diffracts the zero frequency component to form a coherent reference beam (delimited by the double-headed rays in FIG. 3) across the full opening of aperture 20. The incident beam at the aperture 20 is, therefore, the sum of the coherent reference beam from mask 18 and the modulated components (such as the cone 31 component) falling within the aperture 20.
Although the optical mask 18 is shown in FIG. 3 positioned in the positive X axis direction relative to the spatial light modulator 16, the mask can be located in general any place between source 15 and a position in front of detector 19. Specifically, the mask 18 can be located before or after modulator 16 and before or after lens 17. If mask 18 is located in a positive X axis direction such that x is greater than some value x1 as hereinafter defined, then the reference beam will not appear over the full detector aperture and therefore the bandwidth of the output signal on line 14 will be restricted.
In order to further explain the coherent detection operation of the present invention, a mathematical model of FIG. 3 is described. This model assumes a weak acousto-optic interaction for the spatial light modulator 16 so that the diffracted light amplitude in modulated beam 23 is linearly related to the input information signal amplitude S(t).
The acoustic wave in the modulator 16 is defined to be propagating in the -Z axis direction and imposes a dielectric modulation ε proportional to S(t+z/v) where t is time, z is the Z axis coordinate and v is the velocity of the wave in the modulator 16 along the Z axis. Also, the optical beam 22 incident on the modulator 16 is defined to propagate in the XZ plane with a Y axis polarization, and all spatial variations in the Y axis direction may be ignored. Finally, the incident optical beam 22 is defined to propagate through free space at an angle φi to an axis normal to a plane through modulator 16 such that the diffracted energy of the modulated optical beam is concentrated in the m=-1 diffraction order with a negative doppler shift. The desired angle, φi, is obtained, for example, when modulator 16 is rotated in the counter-clockwise direction by the angle φi as shown hereafter in FIG. 4. With these defined conditions, the diffracted optical amplitude E-1 in the m=-1 diffraction order for the beam 31 from modulator 16 has a free space representation which can be described in the X axis plane, X=0, through the spatial light modulator 16 as follows:
E-1.sbsb.[X=0] =CW(z)S+ (t+z/v)e-j2(π/λ.sbsp.L.sup.) sin φ.sbsp.iz-j2πf.sbsp.Lt Eq.(1)
In Eq.(1), C is a complex constant, W(z) is the spatial apodization of the window of acousto-optic modulator 16, and λL is the free space wavelength of source beam 22. The plus subscript for the signal S+ (t+z/v) is used to signify that the diffracted optical beam 23 has a negative doppler shift. The analytic signal S+ (t+z/v) may be expressed in terms of the Fourier transform, S(fa), of the input signal as follows: ##EQU1##
To clearly see that Eq.(1) contains a negative doppler shift, Eq.(2) is substituted into Eq.(1) to derive Eq.(3) as follows: ##EQU2## The optical time frequencies in Eq.(3) are given by fL -fa where fa >0 so that the dopper shift is negative.
The signal beam optical amplitude E-1 described by Eq.(3) is located a distance d in front of lens 17 in FIG. 3. In the back focal plane 33 (Fourier transform plane) of the lens 17, the signal beam optical amplitude ESF is described by the spatial Fourier transform of Eq.(3) multiplied by a quadratic phase factor yielding: ##EQU3##
In Eq.(4), z' is the spatial Z axis coordinate in the Fourier transform plane, λ is the average optical wavelength and F is the lens 17 focal length. By inserting Eq.(1) into Eq.(4) and substituting the following normalized and displaced Fourier transform variable: γ=z'/λF+sin φi /λL, the signal beam optical amplitude ESF in the Fourier transform plane is expressed as follows,
ESF =CW(γ)�[vS+ (γv)ej2πγvt ]e-j2πf.sbsp.Lt Eq.(5)
For Eq.(5), W(γ) is the spatial Fourier transform at the window apodization W(z) while the � symbol denotes convolution over the variable γ. Since the variable γ is proportional to spatial distance in the lens focal plane, the convolution of Eq.(5) acts to spread each doppler-shifted, spectral component vS+ (γv) exp (j2πγvt) of the input signal S(t) over a spatial width in the transform plane determined by W(γ). The number of spatially resolvable spots in the Fourier transform plane is thus limited by W(γ) and the number of spatially resolvable spots is, to a good approximation, determined by the bandwidth product of the apodized spatial light modulator 16.
The signal beam optical amplitude of Eq.(5) is coherently detected by adding the optical reference beam, which is typically not doppler shifted, produced by the mask 18 in FIG. 3. The optical reference beam amplitude ERF in the Fourier transform plane 33 is in general a function of spatial position and may also be expressed in terms of the normalized and displaced Fourier transform plane variable γ as follows:
ERF =ej(π/λF)(1-d/F)(z').spsp.2 R(γ)e-j2πf.sbsp.Lt Eq.(6)
The optical intensity I(γ,t) in the Fourier transform plane in the proximity of the detector aperture 20 is expressed as follows:
I(γ,t)=1/2|ESF +ERF |2 Eq.(7)
The optical intensity distribution defined by Eq.(7) is collected by the large-area photodetector 19 in FIG. 3. The photocurrent output information signal I(t) from the photodetector 19 is given by: ##EQU4##
By combining Eqs. (5), (6), (7) and (8), the output information signal, I(t), is the sum of the three terms in Eq.(9a) as follows:
I(t)=iR +iS (t)+iHET (t) Eq.(9a)
and where the terms in Eq.(9a) are as follows: ##EQU5##
The iR component of the photocurrent defined by Eq.(9b) represents the total reference beam (delimited by double-headed rays in FIG. 3) optical power collected by the photodetector. The reference beam power is independent of time. The iS (t) component defined by Eq.(9c) of the output signal I(t) represents the total diffracted signal beam optical power collected by the photodetector. The iS (t) component of the photocurrent is a low frequency term with the majority of its power near DC and has an absolute maximum time frequency less than (fmax -fmin) where fmax and fmin are the maximum and minimum frequencies of the input information signal S(t). The iHET (t) component defined by Eq.(9d) of the photocurrent is the desired linear output of the detection process. From Eq.(9d) it appears that each spectral component S+ (f) of the input signal S(t) contributes a time frequency component exp (j2πft) to the output component signal iHET (t) so that a linear filter operation exists. To more clearly define the linear filter response, Eq.(9d) is rewritten as follows: ##EQU6## where
H+ (f)=1/2C[W(-γ)�[R*(γ)]] Eq.(10b)
evaluated at γ=f/v.
Eq.(10a) implies that the response for positive frequencies f>0 is defined by H+ (f). From Eq.(10b), it appears that the response H+ (f) is basically equal to R*(f/v) convolved with the inverted window transform W(-f/v).
Eq.(10a) is not quite in the final form of a linear response due to the Re operator (real part of) and the restriction to positive frequencies f>0. To clearly express the linear response for positive and negative frequencies, Eq.(10a) is rewritten using the fact that S(t) is real so that S(f) is equal to S*(-f). Rewriting Eq.(10a) yields the following Eq.(11): ##EQU7## In Eq.(11), the linear frequency response of the optical system from the input signal S(t) to the heterodyne component iHET (t) of the photocurrent is defined by H(f). Furthermore, H(f) is equal to H*(-f) as is required of real valued input and output signals.
Since the heterodyne component iHET (f) of the photocurrent is a linear version of the input signal, the time frequencies f of iHET (t) are bandlimited to the frequency range fmin <f<fmax. As before, fmax and fmin are the maximum and minimum frequencies of the input signal S(t). Thus if the input signal has less than an octave bandwidth so that (fmax -fmin)<fmin, then iHET (t) may be electronically separated from iR and iS (t) by the use of a highpass filter. Typically, a bandpass filter is used at the output instead of a highpass filter since this minimizes the wideband shot noise and rejects signal harmonics which can be present when multi-longitudinal mode lasers are used as the optical source.
The linear response characteristics at the optical processor may be understood by a close examination of H+ (f) from Eq.(10b). The simplest situation occurs with a plane wave optical reference beam, that is, with R(γ) equal to 1. In this case, it is apparent from Eq. (10b) that:
H+ (f)=1/2CW(0) for R(γ)=1 Eq.(12)
In other words, the response H(f) is constant, independent of frequency, so that the system acts like an electrical short circuit from the input to output. In actual practice with R(γ)=1 there is a constant time delay from the input S(t) to the output iHET (t) caused by the constant acoustic transit time from the acoustic transducer boundary to the effective reference beam origin 35 shown at the X=0 plane in the modulator 16.
For other types of processing, a mask or other optical element is typically provided in front of the aperture 20. A blocking mask may be employed, for example, to block one or more selected frequency components thereby removing such components from the output signal.
In FIG. 4, an expanded view of the optical components between the spatial light modulator 16 and the photodetector aperature 20 of the FIG. 3 apparatus is shown. In FIG. 4, the spatial light modulator (SLM) 16, the Fourier transform lens (FTL) 17, the optical mask (OM) 18 and the detector aperture 20 are the same as shown in FIG. 3.
The spatial light modulator 16 is rotated counter-clockwise to the position shown by modulator 16 at an angle φi relative to the X and Z axes. When thus rotated, the diffracted frequency components (triple-headed rays) form an angle θ with the zero frequency component (single-headed rays). The angle θ ranges between θmax and θmin.
In FIG. 4, modulator 16 has a window or aperture 53 with a dimension w in the Z axis direction extending between a first aperture end 51 and a second aperture end 52. The axis of modulation of modulator 16 is in the negative Z axis direction.
The mask 18 is located at some displacement x from the center of the Fourier transform lens 17. In FIG. 4, the optical mask 18', shown in broken line, represents the optimum location when the displacement x is equal to x1 for the optical mask 18. In FIG. 4, the single-headed rays for cone 30 represent the zero frequency beam. The double-headed rays represent the the reference beam diffracted by the mask 18 and which falls within the aperture 20. The triple-headed rays depict a typical cone 31 of one modulated frequency component.
The following TABLE I defines various parameters in FIG. 4.
h(x)=the distance in the Z axis direction, at the X axis displacement x, to the top most part of the optical mask utilized and the distance corresponds to the lowest portion through which the zero frequency beam must pass in order to deflect the reference beam onto the entire detector aperture.
k(x)=the distance in the Z axis direction, at the X axis displacement x, to the bottom most part of the optical mask utilized and the distance corresponds to the highest portion through which the zero frequency beam must pass in order to deflect the reference beam onto the entire detector aperture.
m(x)=the distance in the Z axis direction, at the X axis displacement x, to the bottom of the zero frequency beam.
j(x)=the distance in the Z axis direction, at the X axis displacement x, to the top of the zero frequency beam.
a=the distance in the Z axis direction to the point where the lowest frequency component signal falls within the detector aperture.
b=the distance in the Z axis direction to the point where the highest frequency component signal falls within the detector aperture.
c=the distance in the Z axis direction to the virtual focal point 35 of the reference beam.
d=the virtual focus distance of the reference beam.
e=the distance in the X axis direction between the optical light modulator 16 and the Fourier transform lens 17.
F=focal length of the Fourier transform lens 17.
g=the distance in the positive or negative X axis direction of optical mask 18 from the spatial light modulator 16.
u=the distance in the Z axis direction from the center point 36 of modulator 16 to the virtual image point 35.
w=width in the Z axis direction of the aperture of the spacial light modulator 16.
x=the distance in the X axis direction between the Fourier transform lens 17 and the optical mask 18.
In FIG. 4, the portion of the optical mask 18 which is utilized to deflect the reference beam over the entire aperture is equal to the quantity h(x)-k(x). Note that the extension of the double-headed rays from the aperture 20 back to the virtual image point 35, in the X=0 plane, determines what portion of the optical mask is utilized.
The quantity h(x)-k(x) is the "width" of the cone of the reference beam. The width of the zero frequency cone 30, delimited by the single-headed rays at the displacement x of the optical mask 18, is given by j(x)-m(x). The ratio, Q, of the width of the utilized portion of the optical mask, given by the quantity h(x)-k(x), and the width of the zero frequency cone given by the quantity j(x)-m(x) is the controlling factor in the strength of the reference beam as it appears in the aperture 20 at the Fourier transform plane 33.
The ratio Q will be a maximum at a point where x is equal to x1 at which h(x) is equal to j(x). The optical mask 18' is located at the point where is x equal to x1 so that h(x1) is equal to j(x1).
Although the optical mask 18 can be placed at any location between the spatial light modulator 16 and the plane at x=x1, the reference beam will have the highest strength when x is equal to x1 if the input source beam 22 has a uniform intensity in the Z axis direction. The highest strength of the reference beam occurs at x equal to x1 because, at that location, the highest percentage of the zero frequency beam passes through the utilized portion of the optical mask. The higher the percentage of the zero frequency beam passing through the utilized portion of the optical mask, the higher the reference beam strength at the aperture 20. The high reference beam strength is desirable to maximize the signal-to-noise ratio of the coherent detection process.
When the source beam 22 has a non-uniform intensity distribution in the Z axis direction, for example a Gaussian distribution, then the maximum intensity reference beam is obtained when the optical mask is located at a value of x somewhat less than x1.
The following TABLE II lists typical parameters for the FIG. 4 device in accordance with the present invention.
TABLE II______________________________________bandwidth = 100 M Hzcenter frequency = 200 M Hzφi = 0.56 degreesθmax = 1.39 degreesθmin = 0.84 degreesv = 6.5 � 103 m/secλ = 6.328 � 10 -7 ma = 2.30 cmb = 2.88 cmc = 1.425 cmd = 10 cme = 8 cmF = 50 cmg = 37.8 cmu = 0.2 cmx1 = 27.8 cmh(x1) = 2.35 cmj(x1) = 2.35 cmk(x1) = 1.98 cmm(x1) = 0.90 cm______________________________________
The distance g in FIG. 4 can be measured along the positive or negative X axis such that optical mask 18 is located on the right of (after) or left of (before) spatial light modulator 16. For high frequency applications (500 M Hz or more), mask 18 is typically placed before lens 17 or before modulator 16. In any case, however, the absolute value of g should not be too small since, if g is too small, the reference beam will not have sufficient energy to permit reliable coherent detection when a point source reference source is employed. In the limit, if g equals zero, the reference beam will have zero energy. As a general guide, g should be greater than the quantity given by the following expression,
g>v2 /(fmin 2 λ)
v=velocity of wave in modulator 16
fmin =minimum frequency of input information signal
λ=wavelength of source beam
Although the reference point 35 has been specified as a virtual image point lying in the X=0 plane passing through the center of modulator 16, reference point 35 can be displaced to a location 35' by a distance p displaced in the minus X axis direction such that the virtual image cone (delimited by double-headed broken-line rays) has some width p(z) (measured in the Z axis direction) in the X=0 plane. In general, in order not to introduce additional components into the output signal, the width p(z) of the cone at the X=0 plane should not exceed v/(fmax -fmin) where v is the velocity in the modulator and (fmax -fmin) is the bandwidth of the input information signal. If greater widths for p(z) are employed, distortion components are introduced into the output signal. In many applications, such additional components are undesired. In some applications, however, multiple reference points may be desired.
In FIG. 5, the laser 27, the lenses 28, 29 and 17, and the spatial light modulator 16 are identical to the same elements shown in FIG. 3. Additionally, a beam-splitter 41 is provided to form a reference beam 46 after attenuation in optical attenuator 42. The reference beam 46 is focused through a lens 44 and a spatial filter 45 onto the beam-combining mirror 48. The mirror 48 reflects some of the light beam from lens 44 and filter 45 onto photographic plate 47 where it is combined with the unmodulated beam from the Fourier transform lens 17. The spatial filter 43 appears after the lens 28 to restrict the size of the source beam 22. The spatial filter 45 and the lens 44 are selected so that the reference beam incident on the photographic plate 47 has a virtual image which fully fills the aperture 20 and has a virtual image point 35 in the Z axis direction which appears in the spatial light modulator 16. The shutter 40 is provided for controlling the exposure time of the photographic plate 47. While plate 47 is typically a photographic plate, any type of plate and process suitable for forming a hologram can be employed. Alternatively, a suitable mask or grating can be generated by non-holographic processes such as computer calculation and generation.
With the arrangement of elements as shown in FIG. 5, the photographic plate 47 is exposed for an appropriate period of time. After development of the plate 47, the desired holographic optical mask is ready for use in the apparatus of FIGS. 3 and 4. In actual practice, the spatial light modulator of FIG. 5 serves no purpose and therefore can be removed when optical masks are being exposed.
In FIG. 5, the amount of time delay can be controlled by changing the dimension c. If c is made equal to w, the width of the acousto-optic modulator window, then a minimum time delay is exhibited by the system. Typically, the delay time ranges from a fraction of a microsecond to approximately five microseconds. In one embodiment, x1 was calculated for a minimum time delay to be 752 millimeters. In actual embodiments, with x1 less than 752 millimeters, time delays ranging between 400 nanoseconds and 1.2 microseconds, out of a maximum of five microseconds, were exhibited.
In one example, the plate 47 was Kodak 120-02 glass photographic plates 0.25 inch thick. Such plates exhibit low granularity (grain noise) and high resolving power (greater than 2000 lines/mm). The following are processing steps used for developing the plates:
(1) 7 minutes with gentle agitation in D-19 (400 milliliter of Kodak D-19 concentrate per 2 liters of warm tap water.
(2) 1 minute in 1.3% solution of acetic acid.
(3) 4 minutes in Kodak rapid fix and hardener.
(4) 30 seconds in "Hustler" brand rapid bath hypo-remover solution.
(5) 5 to 10 minutes in running tap water.
The best exposure obtained for the Kodak 120 plates employed approximately 30 microjoules per square centimeter with the ratio of the source beam to reference beam energy approximately 2 to 1.
Although the Fourier transform lens 17 and the spatial mask 18 have been described as separate optical elements which form a reference beam generator means, their functions can be combined into a single optical element within the scope of the present invention. For example, a single optical mask can be formed which performs both the Fourier transform and diffraction functions. In some embodiments, the mask performs only the Fourier transform function with the reference beam derived directly from the source.
Although the detector and detector aperture have been described for simplicity of design as located at the focal distance F from the transform lens, the detector and detector aperture may be located at other locations before or after the focal distance F.
Although the photodetector has been described as a single device with a single output, multiple detectors may be employed. For example, an array of detectors can be located at or near the back focal plane 33, each one for detecting different frequency components of the input signal.
While the invention has been particularly shown and described with reference to the preferred embodiments thereof, it will be understood by those skilled in the art that those changes in form and details may be made therein without departing from the spirit and the scope of the invention.
|Cited Patent
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|Trw Inc
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|Acousto-optic channelizer-based ultra-wideband signal processor
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|Directional display and method of making a mask for a directional display
|Jul 16, 1985
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|Fourier plane recursive optical filter
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|U.S. Classification
|359/298, 708/816
|International Classification
|Cooperative Classification
|European Classification
|Mar 23, 1981
Owner name: PROBE SYSTEMS, INC., 655 NORTH PASTORIA AVE., SUNN
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST.;ASSIGNOR:JACKSON, DAVID W.;REEL/FRAME:003903/0792
Effective date: 19810303
|Nov 20, 1984
|Certificate of correction
|Jan 22, 1987
|Maintenance fee reminder mailed
|Jun 11, 1987
|Fee payment
Year of fee payment: 4
|Jun 11, 1987
|Surcharge for late payment
|Jan 24, 1995
|Maintenance fee reminder mailed
|Jun 18, 1995
|Lapse for failure to pay maintenance fees
|Aug 29, 1995
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Effective date: 19950621

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