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Revenue Recognition and Contract Balances - Disaggregation of Revenue (Details) - USD ($)
$ in Millions
 12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Disaggregation of Revenue [Line Items]      
Net sales $ 5,458.6 $ 4,614.3 $ 3,086.2
United States      
Disaggregation of Revenue [Line Items]      
Net sales 2,872.6 2,466.4 1,700.9
Europe      
Disaggregation of Revenue [Line Items]      
Net sales 1,157.3 958.5 616.9
Asia      
Disaggregation of Revenue [Line Items]      
Net sales 971.5 807.9 597.6
All other      
Disaggregation of Revenue [Line Items]      
Net sales 457.2 381.5 170.8
United States Government      
Disaggregation of Revenue [Line Items]      
Net sales 1,359.9 1,193.1 818.2
Other      
Disaggregation of Revenue [Line Items]      
Net sales 4,098.7 3,421.2 2,268.0
Digital Imaging      
Disaggregation of Revenue [Line Items]      
Net sales 3,110.9 2,412.9 986.0
Digital Imaging | United States      
Disaggregation of Revenue [Line Items]      
Net sales 1,416.6 1,082.6 387.0
Digital Imaging | Europe      
Disaggregation of Revenue [Line Items]      
Net sales 749.7 567.8 245.2
Digital Imaging | Asia      
Disaggregation of Revenue [Line Items]      
Net sales 637.8 510.3 310.7
Digital Imaging | All other      
Disaggregation of Revenue [Line Items]      
Net sales 306.8 252.2 43.1
Digital Imaging | United States Government      
Disaggregation of Revenue [Line Items]      
Net sales 619.1 515.9 120.9
Digital Imaging | Other      
Disaggregation of Revenue [Line Items]      
Net sales 2,491.8 1,897.0 865.1
Instrumentation      
Disaggregation of Revenue [Line Items]      
Net sales 1,254.0 1,166.9 1,094.5
Instrumentation | United States      
Disaggregation of Revenue [Line Items]      
Net sales 554.5 512.6 471.1
Instrumentation | Europe      
Disaggregation of Revenue [Line Items]      
Net sales 311.5 298.5 279.2
Instrumentation | Asia      
Disaggregation of Revenue [Line Items]      
Net sales 267.1 247.5 238.9
Instrumentation | All other      
Disaggregation of Revenue [Line Items]      
Net sales 120.9 108.3 105.3
Instrumentation | United States Government      
Disaggregation of Revenue [Line Items]      
Net sales 108.1 91.6 80.6
Instrumentation | Other      
Disaggregation of Revenue [Line Items]      
Net sales 1,145.9 1,075.3 1,013.9
Aerospace and Defense Electronics      
Disaggregation of Revenue [Line Items]      
Net sales 682.4 628.7 589.4
Aerospace and Defense Electronics | United States      
Disaggregation of Revenue [Line Items]      
Net sales 494.6 469.0 429.4
Aerospace and Defense Electronics | Europe      
Disaggregation of Revenue [Line Items]      
Net sales 96.1 92.1 92.4
Aerospace and Defense Electronics | Asia      
Disaggregation of Revenue [Line Items]      
Net sales 65.3 48.6 46.6
Aerospace and Defense Electronics | All other      
Disaggregation of Revenue [Line Items]      
Net sales 26.4 19.0 21.0
Aerospace and Defense Electronics | United States Government      
Disaggregation of Revenue [Line Items]      
Net sales 266.3 227.2 229.9
Aerospace and Defense Electronics | Other      
Disaggregation of Revenue [Line Items]      
Net sales 416.1 401.5 359.5
Engineered Systems      
Disaggregation of Revenue [Line Items]      
Net sales 411.3 405.8 416.3
Engineered Systems | United States      
Disaggregation of Revenue [Line Items]      
Net sales 406.9 402.2 413.4
Engineered Systems | Europe      
Disaggregation of Revenue [Line Items]      
Net sales 0.0 0.1 0.1
Engineered Systems | Asia      
Disaggregation of Revenue [Line Items]      
Net sales 1.3 1.5 1.4
Engineered Systems | All other      
Disaggregation of Revenue [Line Items]      
Net sales 3.1 2.0 1.4
Engineered Systems | United States Government      
Disaggregation of Revenue [Line Items]      
Net sales 366.4 358.4 386.8
Engineered Systems | Other      
Disaggregation of Revenue [Line Items]      
Net sales $ 44.9 $ 47.4 $ 29.5