AM-derivative spectrophtometry with high signal-to-noise ratio for UV-Vis spectrophotometer

Tingting Luo, Sheng Yang*, Yuhang Chen*, Xiangcheng Chen, Jiamei Ding, Wenhao Huang

Department of Precision Machinery and Precision Instrumentation University of Science and Technology of China, Hefei, China

Corresponding author: yangs@ustc.edu.cn; chenyh@ustc.edu.cn;

Abstract— This paper proposes a new method: amplitude modulation derivative (AM-derivative) spectrophotometry for UV-Vis spectrophotometer achieved by differentiating the spectral signal modulated to a higher frequency. Both simulating signals and real spectral signals were verified. Values of SNR were obtained (38.87 for AM-derivative spec-trophotometry while approximately 0 for conventional derivative spectrophotometry) in simulating experiment. Values of LOD were obtained (0.0129 for AM-derivative spectrophotometry while 0.0134 for conventional derivative spectrophotometry) using paracetamol in real spectral experiment. Results show that AM-derivative spectrophotometry significantly suppresses the noise without weakening the useful signal, therefore supply a better Signal-to-Noise Ratio and LOD.

Keywords-derivative spectrophtometry (DS); AM-derivative Spectrophtometry; Signal-to-Noise Ratio (SNR); detection of limit (LOD); double-side band suppressed-carrier (DSBSC)

I. INTRODUCTION

UV-Vis spectrophotometry is one of the most widespread techniques in analysis of pharmaceutical [1], food [2], cosmetics [3] biological sciences chemical engineering and so on due to its rapidity, low-cost instruments, and higher accuracy and reproducibility [4]. Derivative spectrum, compared with traditional zero-order spectrum, usually improves resolution bands, eliminates the in�uence of background or matrix, since it enhances the detectability of minor spectral features [5]. Therefore, derivative spectrophotometry has found wide application in analysis of multicomponent samples [6] [7].

The procedure of differentiation in derivative spectrophotometry degrades the signal-to-noise ratio [9], As a result, the higher differentiation order is, the worse signal-to-noise ratio tends to be, which means a dissatisfied detection of limit (LOD). Thus, we proposes a new method: AM-derivative spectrophotometry for UV-Vis spectrophotometer, a double-sideband suppressed-carrier (DSBSC) method is chosen for amplitude modulation because of its mathematical simplicity during differentiation [9]. In the end, we envisioned a UV-visible spectrophotometer, which can obtain real-time derivative spectrum of better SNR and LOD values.

II. THEORETICS A SNR deterioration of derivative spectra

For the reveal of how the Signal-to-Noise Ratio degrades, we denote high-frequency signal as ����� �

���� �� , low-frequency signal as ����� �

�������, then the signal mixed with high-frequency part and low-frequency part is denoted as ���� ����� �� � ������� . Differentiating the mixed signal����, we obtain: ����� � ����� �� � ��������

� � ��� ����� �� � ��� ��������

1 It can be concluded that the amplitude of high-frequency signal nw is enhanced much more than the amplitude of

low-frequency signal mw , which explains the reason why the SNR degrates after traditional derivative spectrophotometry.

B. AM-derivative Spectrophtometry

Based on double-side band suppressed-carrier (DSBSC) theory, AM-derivative spectrophotometry amplitude modulates the low-frequency spectral signal and then differentiates it at high frequencies. Denote the carrier wave as ���� � ������� , then DSBSC modulation is performed by multiplying the modulation signal m (t) with the carrier wave c (t) as:

���� � ��� � [���� �� � �������]� ��������

� ����� �� � ������ � �������� � ������

(2)

��

����! � !�� � � ��! � !�� �� �

"#

�[��!� �

!�� � � ��!� � !�� �] (3)

Differentiating the amplitude-modulated wave as (3) shows, produces:

����� � ����� � ���

$��! � !�� � ����! � !�� �

� �! � !�� � ����! � !�� �� �

���������������������������������������"#

�[�!� � !�� � ����!� � !�� � �

���������������������������������������!� � !�� � ����!� � !�� �]

2012 International Conference on Biomedical Engineering and Biotechnology

978-0-7695-4706-0/12 $26.00 © 2012 IEEE

DOI 10.1109/iCBEB.2012.53

37

The above statement shows the process of AM-derivation, while the mixed signal after AM-derivation consists of four high-frequency waves, whose are �! % !�� and �!� % !��.

We assume high-frequency signal as noise signal, low-frequency signal as usefull spectral signal, and mixed signal as the real-test spectral signal. As limited by the linear range of spectrophotometer, we can choose the amplitude of carrier wave C as 1. Thus, when the carrier wave frequency !� we chosen is far greater than ! and !� , amplitude of the signal consisted of four high-frequency waves are all on the lever of�!�, amplitude of high-frequency signal and low-frequency signal after AM-derivation is to be the same, which permits a better SNR. Moreover, the greater !� is chosen, the better signal-to-noise ratio will be.

The above process of AM-derivative produces an undesired component ����� � ����� � ����� � ��� �

���� � ���� ����� � ��� is a desired part, we can obtain ����� from it after further demodulate, while ���� � ���� is an undesired part, it can be removed by adding ����� � ���� to ����� � ����� , and the component ����� � ���� can be generated, as is shown in Fig 1. In general, the method of AM-derivative spectrophotometry successfully avoids the degradation of SNR caused by traditional derivative spectrophotometry.

Figure 1. Flow chart of AM-derivative method.

III. EXPERIMENT A. Simulate experiment 1 Generation of simulate signal Simulate signal was generated using MATLAB 2008a,

and all the procedure was modelled using MATLAB 2008a, according to the principles discribed above.

2 Processing of simulating signals without noise Sine wave is chosen as the simulating signals, both

methods was applied. Results are shown in Fig 2, AM-derivative spectrophotometry can process simulating signals without weakening and deformation as well as traditional derivative spectrophtometry, which showes that AM-derivative spectrophotometry has considerable

reliability.

Figure 2. AM-derivation of sine data(a). Traditional derivation of sine

data(b).

3 Processing of simulating signals with noise White noise was added to simulating signals, of which

SNR is 80dB. In Fig 3(A), traditional derivative spectrophtometry can’t get satisfactory result, and the SNR of output signal is �& � '(�)�* dB approximately 0). While in Fig 3(B), AM-derivative spectrophotometry lead a very satisfactory result, whose SNR of output signal is 38.87 dB. SNR both degraded in the two methods, however, SNR obtained from AM-derivation is obviously better than that from traditional derivation.

4 Relationship between SNR and carrier frequency and sampling frequency

Fig 4(A) shows the spectral profile after AM-derivation at a carrier frequency of 2KHZ, while Fig4-B at a carrier frequency of 10KHZ. Result closely match the theoretical prediction, which shows the higher the carrier frequency get, the better the result will be.

Figure 3. Direct derivation of sine data added with white noise

(A).AM-derivation of sine data added with white noise (B)

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Figure 4. AM-derivation of sine wave (fc=2KHZ)(A). AM-

derivation of sine wave (fc=10KHZ)(B)

We can conclude that SNR varies when carrier frequency changes, as shown in Fig 5. Moreover, an increasing sampling frequency can also improve SNR.

Sampling frequency (fs) is a rate used in the amplitude modulation of carrier signal and simulating signal. As shown in Fig 6, SNR improves as the sampling frequency increases at a given carrier frequency. All three curves demonstrated that SNR increases as carrier frequency increases.

Figure 5. SNR experimentally obtained at different carrier frequencies.

Figure 6. Variation of SNR as a function of carrier frequency and

sampling rates.

B. Spectra experiment 1 Apparatus and reagents

All experiments were performed on UV-2100PC spectrophotometer (Shanghai UNICO Company). The spectral bandwidth is 5nm, the wavelength accuracy is ±2.0nm and the wavelength repeatability was 1.0nm. Electronic balance (Ohaus International Trade Co., Ltd). Paracetamol (Ruibio biological Trade Co., Ltd).

2 Getting of real spectral signal Stocking solution of paracetamol was prepared by

dissolving 0.01g of the solid in redistilled water of 100mL, then obtain stocking solution of 100ug/mL. Working solution of 1 μg/mL, 1.6 μg/mL, 2 μg/mL, 5 μg/mL, 8 μg/mL, 10 μg/mL, 12 μg/mL, 15 μg/mL were obtained by diluting the stocking solution prepared above. We got six absorption spectrums between 220 nm and 260nm, and in order to simulate analog signals inside the circuit, white noise was added to the spectrum we obtained.

3 Processing of real spectral signals To determine the value of LOD, we deal with the real

spectrums using both methods, and then we got derivative spectrums of eight groups. We can draw standard curves with those eight groups: pick the peak point at �=226 nm of every derivative spectrum, then the derivative value and concentration of the standard sample together can form a data point (A i,Ci) (i=1,2…8). Finally, least-squares linear fitting was done, then standard line can be drawn: C=bA+a shown in fig8 A and B, LOD value can be got from the line. In fig 8, sign’+’ representatives the original eight data points (A i, Ci) (i=1, 2…8), while

representatives the line after Least-squares fitting.

As is shown, after traditional derivative spectrophotometry, point (0.02, 2) and (0.008, 5) deviate from the fitted line apparently, indicating that noise of this method is relatively large. The result shows better after AM-derivative spectrophotometry, both (0.00029107, 2) and (0.0021, 5) are on the line. The LOD were calculated respectively, which is shown in table 1.

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Figure 7. Least-squares fitting line after traditional first-order derivative

spectrophotometry(A). Least-squares fitting line after traditional first-order derivative spectrophotometry(B)

TABLE 1 Compared of two methods’ Results

Methods Table Column Head

SNR(dB) LOD(μg/mL) Conventional Derivation

0 0.0134

AM- differentiation 38.87 0.0129

Based on this theory and experimental results, integrated with AM-derivative circuit, it is expected to develop the innovative UV-visible spectrophotometer, which can obtain real-time derivative spectrum of better SNR and LOD values.

Figure 8. Simplified structure of UV-Vis spectrophotometer with AM-

derivative circuit.

IV. RESULT AND DISCUSSION The result shows AM-derivative spectrophotometry

for UV-Vis spectrophotometer is valid. Both simulating signals and real spectral signals were processed, AM-derivative spectrophotometry suppresses the noise significantly without weakening the useful signal, permitting a better Signal-to-Noise Ratio, which means a lower detection limit (LOD), compared to traditional derivative spectrophotometry.

This method may get better results in low concentration analysis and multicomponent analysis due to its advantages. In the near future, UV-Vis spectrophotometer consisted of AM-derivative system may take the place of expensive chromatography in the analysis of low concentration and multicomponent with less expenses.

ACKNOWLEDGMENT

Thanks are due to Prof. Yuhang Chen and Prof. Wenhao Huang for funding to attend the meeting.

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