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Business Segments (Narrative) (Details)
$ in Millions
12 Months Ended
Jan. 02, 2022
USD ($)
segment
product_line
Jan. 03, 2021
USD ($)
Dec. 29, 2019
USD ($)
Segment Reporting Information [Line Items]      
Number of reportable segments | segment 4    
Net sales $ 4,614.3 $ 3,086.2 $ 3,163.6
Sales between business segments 20.2 23.4 30.3
United States Department of Defense      
Segment Reporting Information [Line Items]      
Net sales 876.6 578.4 545.5
Countries Other Than United States      
Segment Reporting Information [Line Items]      
Net sales 2,147.9 1,385.3 1,391.6
Countries Other Than United States | Domestic Operations      
Segment Reporting Information [Line Items]      
Net sales $ 723.9 546.8 638.0
Instrumentation      
Segment Reporting Information [Line Items]      
Number of product lines | product_line 3    
Net sales $ 1,166.9 1,094.5 1,105.1
Aerospace and Defense Electronics      
Segment Reporting Information [Line Items]      
Number of product lines | product_line 1    
Net sales $ 628.7 589.4 690.1
Digital Imaging      
Segment Reporting Information [Line Items]      
Number of product lines | product_line 1    
Net sales $ 2,412.9 986.0 992.9
Engineered Systems      
Segment Reporting Information [Line Items]      
Number of product lines | product_line 1    
Net sales $ 405.8 $ 416.3 $ 375.5
Engineered Systems | Net sales | Contract type | Fixed-price Contract      
Segment Reporting Information [Line Items]      
Sales to individual countries outside the United States 47.00%    
Engineered Systems | Minimum | Net sales | Contract type | Fixed-price Contract      
Segment Reporting Information [Line Items]      
Sales to individual countries outside the United States 45.00%    
Engineered Systems | Maximum | Net sales | Contract type | Fixed-price Contract      
Segment Reporting Information [Line Items]      
Sales to individual countries outside the United States 55.00%