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Create a row Mat for each data,then use hconcat to concatenate them in a final image. It should be something like (untested code):

Mat result;
double *data;
while(capturing){
    data=GetSpectrometerData()
    Mat datMat(1,2048,CV_64F,data);
    hconcat(result,datMat,result);
}
imshow("Captures spectra",result);