Figure 5 show the

$R(x,y)$ images for different anti-BSA concentration. Similar to the result of dynamic measurement for BSA injection, the analytes are not sufficient to form a single layer but several aggregations for low anti-BSA concentrations. As anti-BSA concentration increases up to 1 μg/mL, most of the pixels are deposited with at least one layer of the analytes, and the non-uniform distribution still exists.

Figure 5b shows statistic distribution of

$R(x,y)$ values for various concentrations. There is a small deviation of the distribution when the concentration is low. When the concentration increases, the deviation increases. This verifies the non-uniform interactions between BSA and anti-BSA proteins. From the mean values

$M$ of the distribution, the detection limit is around 10 ng/mL. For low concentrations below 10 ng/mL, the difference of

$M$ remains obscured because the signal may be mixed up with unwanted noises by averaging the non-uniform responses. Based on the visualized distribution images in

Figure 5a, it is reasonable to deduce that the detection limit can be improved by an analysis method which is effective in eliminating unwanted noises especially for low concentrations. By simply adding a discriminant based on the SIA, a threshold value

$T$ is introduced and the pixels for

$R(x,y)<T$ are considered as noises. The newly built equation is expressed as

${R}^{\prime}(x,y)\text{}=\text{}\left[R\right(x,y)T]\times R(x,y)$, where

${R}^{\prime}(x,y)=R(x,y)$ if

$R(x,y)>T$, otherwise,

$R(x,y)=0$. To test the threshold effect, we applied different

T values in the analysis.

Figure 5c shows the effect of the threshold on the statistic distribution of “

R(x,y)”, where S0, S1, S2 and S3 denote the

$T$ values as the average plus 0, 1, 2 and 3 times standard deviation of SIA values of pixels.

Figure 5d show the resultant

$R(x,y)$ images using S1 for different concentrations. The signal-to-background ratio is substantially improved for low-concentration images, while high-concentration images remain the same. Such a threshold method can help enhance the detection limits for low concentrations due to the effective elimination of background noise.

Figure 6 shows mean value

$M$ of

$R(x,y)$ and standard deviation for different concentrations and threshold values; we plot the deviations for the measurements in different SPR chips. The control signal was measured in DI water without dissolving any anti-BSA. In this plot, the standard deviation was obtained from the results of different SPR chips. Due to the fabrication errors between chips, the SPR response had a large deviation for different chips. It is noted that the threshold value plays an important role in the image analysis. For larger

$T$ values (S2 and S3), the threshold is too large to remove the real SPR signals. As a result, the SPR signals are reduced for high concentrations and close to zero for low concentrations. The optimal threshold value is around one standard deviation of the control experiments. In this case, undesired noises are efficiently eliminated, also substantially improving the dynamic range, as shown in

Figure 6. The signal range from 10 ng/mL to 10 μg/mL is increased by about 1.6 times. Considering only the stability of the measurement system, the LOD of anti-BSA, defined by 3 × STD, was 2.13 ng/mL for S0 and reduced to 1.23 ng/mL for S1. However, when considering the large variation of SPR chips, the LOD was increased. Nevertheless, using the threshold method, the LOD can also be improved as compared to the simple SIA process. In

Figure 6, the LODs for S0, S1 and S2 were 461, 279, and 110 ng/mL, respectively. This shows improved LOD using our proposed method.